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How do you write an modus ponens in symbols using letters and true-functional connectives?
Wiki User
∙ 11y ago
Modus Ponens can be written in the following way symbolically:
p --> q
p
Therefore q
Where the lowercase letters can be any statement, "-->" represents an arrow for a conditional statement, and use three dots arranged in a triangle to represent "therefore."
Wiki User
∙ 11y ago
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What is the proof of the modus ponens not by the truth table?
1)p->q 2)not p or q 3)p 4)not p and p or q 5)contrudiction or q 6)q
How do you use the rules of inference to construct formal proofs?
The point of a formal proof of validity is to get back to the conclusion of a syllogism in as few steps as possible. Let's say we have the syllogism: 1. P>Q (that's supposed to be a conditional...) 2.P 3.Q>R /.'.R What you want to do is keep going with the syllogism. You can use steps 1, 2,and 3, but you cannot use the conclusion. How you use them is try to find which rules of inference start with any of your premises. For instance, step #1, P>Q and step #3, Q>R are the first two premises in the Hypothetical syllogism. So you could make step #4 P>R. Next to this step you will put what is called the 'justification', which would look something like this: 1,3 H.S. (which means: I used steps 1 and 2 and a hypothetical syllogism to make this step). Now we can use the step we just made in a Modus Ponens. This would use steps 4 and 2, and would look like this: R. Do you recognize that? That was our conclusion. We have now finished this formal proof of validity. Here's what the whole thing looks like: 1. P>Q 2.P 3.Q>R /.'. R 4.P>R 1,3 H.S. 5.R. 4,2 M.P. (If you want to look like you really know what you're doing, you will want to put Q.E.D. at the end of a formal proof. That's what the real logicians do). Hope this helps!! (By the way, I'm 13.) :D
What are some math terms?
AAbacus in Various Number SystemsAbelian groupAbscissaAbsolute GeometryAbsolute valueAbsolute value of a complex numberAbsorbtion identityAbundant NumberAcute angleAcute triangleAdams' CircleAdams' Method of ApportionmentAdditionAddition Formula for SineAdditive InverseAdditivityAdjacencyAffine-regular PolygonAffine GeometryAffine SpaceAffine TransformationAffirmative Action ProblemAlabama ParadoxAlexander the GreatAlgebraic numbersAlgorithmAliquot partAll Triangles Are IsoscelesAlternate AngleAlternating groupAltitudeAn Airline ProblemAnallagmaticAnalog gadgetsAngleAngle BisectorsAngle of incidenceAngle of reflectionAngle preservation propertyAngle TrisectionAngular distanceAnnulusAn Old Japanese TheoremAnticenter of a QuadrilateralAntichainAntichain in lexicographic orderAnticommutativity Anticommutative quasigroupAnticomplementary Triangle Anticomplementary TriangleAntiequilic QuadrilateralAntihomologousAntiparallel AntiparallelAntipedal triangleAntisymmetryApollonian GasketApollonian CirclesApollonian Circles Theorem Apollonian Circles TheoremApollonian Family of CirclesApollonius ProblemApollonius' TheoremApportionment ProblemArbelosArc (in circle)Archimedes' Law of the LeverArchimedes of SyracuseArchimedes TriangleArchimedes' LemmaArchimedes' MethodArchimedes' spiralArchimedes' Squaring of ParabolaArchimedes' Twin CirclesArea of a ParallelogramArea of a RingAreal CoordinatesArgand DiagramArgument of a Complex NumberArithmetic mean Arithmetic-Geometric Mean InequalityArithmetic Operations in Various BasesArithmetic ParadoxesArithmetic SeriesArticulation (node) of a graphASAAssimilation IllusionAssociativity AssociativityAssociatesAstroid AstroidAsymmetric Propeller Napoleon's PropellerAsymmetryAttractive PointAutomatonAutomorphismAxiom of ChoiceAxiom schemaAxiomatic CompletenessAxis of HomothetyAxis of Symmetry of a ConicBBachet's Magic TrickA Baffling PredictionBalinski and Young's Impossibility TheoremBanach-Tarski DecompositionBankoff's ConundrumBanzhaf IndexBarbier's Theorem Barbier, The Theorem ofBarcode EncodingBarycenter, barycentric coordinates 3 Jugs Problem3 Glasses Problem in Barycentric CoordinatesBarycentric coordinates and Geometric ProbabilityBase Converter Algorithms for Base ConversionConversion of Fractions in Various BasesBasic Rigid Motions of the PlaneBasil Rennie's LemmaBayes' TheoremBear cubs problemBeatty SequencesBeecroft's TheoremBenford's LawBenham's TopBernoulli TrialsBernstein theoremBertrand's ParadoxBevan's Point and TheoremBézout's IdentityBézout's LemmaBicentric QuadrilateralBicolor Towers of HanoiBijectionBilateral DiagramBimedians (in a tetrahedron)Binary Encoding with the Stern-Brocot treeBinary Euclid's AlgorithmBinary RelationBinary SystemBinet's FormulaBinomial CoefficientBinomial DistributionBinomial TheoremBipartite graphThe Birthday ProblemBisectal CircleBisecting arcsBisecting a shapeBitwise shiftBitwise boolean operationsBlithe 12 puzzleBlivetBlock DesignBogus Nim Bogus NimBolzano Theorem Bolzano Theorem, proofBooklandBottema's theoremBoundBound VariableBoundary pointBounded DistanceBrahmagupta's TheoremBrahmagupta's formulaBraids TheoryBraikenridge-Maclaurin TheoremBreaking Chocolate BarsBrianchon's theoremBrick Wall IllusionBride's ChairBrocard angleBrocard circleBrocard diameterBrocard pointsBroken Chord TheoremBrouwer's Fixed Point TheoremBuffon�s Needle Problem Math SurprisesBulging lines illusionButterfly Theorem A Better Butterfly TheoremTwo Butterflies TheoremThe Lepidoptera of the CirclesByzantine BasketballCCabart's CollinearityCake cuttingCalendar MagicCalissonCandy's TheoremCanonical Equation of ConicsCanterCantor FunctionCantor set Cantor set of positive measureC0 - C0 = [-1, 1]Cantor's linesCantor's pointCantor's theoremCantor-Bernstein-Schroeder theoremCardinal Cardinal NumbersCardioid Hearty Munching on CardioidsCarnot's TheoremCarnot's TheoremCarnot's Theorem (Generalization of Wallace's Theorem on simsons)Carpets TheoremCartesian coordinates Cartesian coordinate systemCassini's identityCauchy's inequalityCauchy's limitCauchy sequenceCavalieri's PrincipleCayley's LinesCayley TableCayley's TheoremCeiling FunctionCellular AutomatonCenter CirclesCenter of InversionCentipedeCentral AngleCentral SimilarityCentral Limit TheoremCentroid Centroid, a Characteristic Property OfCircle of Similitude (of three directly similar figures)Circle of Similitude (of two circles)Ceva's Theorem Ceva's Theorem and Fibonacci BamboozlementThe Menelaus theoremTrigonometric Form of Ceva's TheoremCeva is equivalent to Menelaus ICeva is equivalent to Menelaus IICevianCevian NestCevian Triangle Cevian TriangleChanging ColorsChaosCharacteristic Constants of the n-LineCharacteristic functionChasles' TheoremChebyshev polynomialsChecker - jumpingChevalier de M�r�'s ProblemChinese Remainder TheoremChord (in circle)Chronology of updatesChvatal's Art Gallery TheoremCircleCircle of ApolloniusCircle of ConcernCircle of InfluenceCircle-Stacking TheoremCircuit, same as cycleCirculant Matrix Circulant Matrix: exampleCircular CoordinatesCircular Poggendorff IllusionCircumferenceCircum-orthic TriangleCircumcenter Existence of 1Circumcevian TriangleCircumcircleCircumpedal TriangleCircumradiusCircumscriptible PolygonCity-block distanceClassification of TrianglesCleavance centerCleaverClifford's ChainClifford's LemmaClinantClosed intervalClosed setClosed walkClosureCoalitionCoaxal circlesCoaxal Circles TheoremCoincidenceCollatz ConjectureCollinear pointsCollage TheoremColumn vectorCombinationCombinatorial ProofsCommon FractionCommon Notions of EuclidCommutative groupCommutativityCompact setsCompactificationComparing complex numbers.Complementary anglesComplementary eventComplementary sequencesComplete graph Complete graphComplete orderComplete QuadrangleComplete Quadrilateral Complete Quadrilateral, the Theorem ofDiagonals of the complete quadrilateralCompletenessCompletion of a SpaceCompleting the Square and Quadratic FormulaComplex numbersComplex product of Complex NumbersComplex Projective LineComposite numberCompositionCompound InterestConcatenationConcentric circlesConcentric polygonsConcurrent linesConcyclic PointsConditional ProbabilityConeConformalCongruent setsCongruence Modulo a NumberConic SectionsConjugate complex numbersConjugate coordinatesConjugate Diameters in EllipseConjugate families of circlesConjugate pointsConjunctionConnected component of a graphConnected graphConnected setConsecutive Isosceles DecompositionConsistencyConstant ChordConstant Random VariableConstant width, shapes ofConstructible NumbersConstruction problemConstruction with the Compass Only Rusty Compass Construction of Equilateral TriangleContact TriangleContentContinuityContinued fraction Continued Fractions on the Stern-Brocot TreeContinuous Line IllusionContinuumContinuum HypothesisContraction Mapping TheoremConvergentConvergent SequenceConvergent SeriesConverse theoremConvex hullConvex shapeConvolution ConvolutionConway's CircleCoolidge theoremCoordinateCopernicus' Theorem Proof of Copernicus' TheoremCoprimeCosine Rule Another derivationIn a vector spaceCountable setsCounting: The Beginning of Mathematics Let Them CountCounting numbersCovering A Chessboard With DominoCritical PlayerCross productCrosscapCrossing Diagonal MethodCrossing Number of a GraphCrossoverCross-RatioCrossed-Lines Construction of Shapes of Constant WidthCurveCTK Exchange, theCurry's ParadoxCurvilinear triangleCutting pipesCycle (a permutation)Cycle (on a graph), same as circuitCyclic quadrilaterals Brahmagupta's TheoremFour Concurrent Lines in a Cyclic QuadrilateralIncenters in Cyclic QuadrilateralRemarkable Line in Cyclic QuadrilateralCycloidsCyclotomic EquationCylinderDDartData StructureDate GameDay's Sine Illusionde Bruijn cycleDecimal numeralDecomposition by DissectionDefect of a Langford SequenceDeficient NumberDegree of a vertexDelboeuf IllusionDelian Problem Delian Problem SolvedDeliberate AmbiguitiesDeltahedronDeltoid Steiner's Curvede Moivre's formula de Moivre's formulaDe Moivre numbersde Morgan's FormulasDemagogueryDenuminatorDependent EventsDense setDensity functionDensity (of a binary relation)DerangementDesargues' TheoremDescartes' formulaDescartes' Rule of SignsDevil�s pitchforkDiagonal CountDiagonal matrixDiagonal processDiagonal TriangulationDiagonals of the complete quadrilateralDiameter of a circleDiameter of a triangulationDiameter of a convex shapeDihedral SymmetryDifference of two setsDigital RootDigits, fun withDigraphDilationDimensional AnalysisDirect productDirect sumDirected AngleDirectly Congruent FiguresDirectly EquidecomposableDirectrix Directrix of an EllipseDisappearing Lines (puzzle)Disconnected graphDiscovery of Duane DeTempleDiscriminant of Quadratic Expression Discriminant of Quadratic Equation Disjoint EventsDisjunctionDisjunctive RuleDisjunctive sum of gamesDistanceDistance Between StringsDistance FormulaDistance From a Point to a Straight LineDistance on the sphereDistance to the HorizonDistorted Lines IllusionDistributive LawsDivergent SeriesDivide a segment into n equal partsDivisibility by 3Divisibility by 7Divisibility by 9Divisibility by 11Divisibility by 81Divisibility CriteriaDivisor of zerod'Ocagne's identityDodecagonDot Patterns and Sierpinski GasketDo you know that...Dot productDouble FactorialDouble Generation TheoremDouble negativeDouble angle formula for sineDoubling the CubeDouglas' TheoremDrawing circles and ellipsesDroodlesDroz-Farny CirclesDroz-Farny Line TheoremDual to Pappus' TheoremDualityDuality PrincipleDucci Sequence Ducci SequenceDuplication of the CubeDumb ParrotDynamic Construction of Ellipse and Other CurvesE8-connectednessEAN-13 encodingEarEccentricityEdgeEgyptian MultiplicationEgyptian Triangle Egyptian Triangle By Paper FoldingEigenvalueEigenvector Eigenvectors by InspectionEliminandEmpty setExterior Angles formed by a secant and parallel linesEpicycloidsEppstein's pointsEquationEquation of a Straight Line Through Two PointsEquation of a Straight Line with Two InterceptsEqual Incircles TheoremEqualityEquiangular polygon A Property of Equiangular PolygonsEquichordal points: Just Do ItEquidecomposable shapesEquilateral polygonEquilateral triangleEquilic QuadrilateralEquivalence RelationsThe Erdös-Mordell InequalityEuclid's Algorithm Almost Integers, Euclid's AlgorithmExtension of Euclid's AlgorithmEuclid's GameEuclid's proof of the Pythagoras' TheoremEuclidean distanceEuler LineEuler-Nagel LineEuler's CharacteristicEuler's Formula Euler's FormulaEuler's FormulaEuler's Formula and Poncelet PorismEuler's Function and Congruence TheoremEuler-Mascheroni ConstantEuler pointsEuler's TheoremEuler's PointsEuler's TriangleEuler walkEven permutationEven vertexEvolution of Algebraic SymbolismExcenterExcentral triangleExcircleExistential ImportExistential QuantifierExscriptible QuadrilateralExtended Argument of a Complex NumberExtension FieldsExtension of Euclid's AlgorithmExterior Angle Theorem - an appreciationExternal Bisector External Angle BisectorExternal productExternal SymmedianExternal Tangent to Two Circles"Extra-geometric" proofs of the Pythagorean TheoremExtremeExtreme points of convex figuresExtreme Value TheoremEyeball TheoremEye Opener SeriesF4-connectedness4 Knights4 travellers problem4x4 coloring problemFactorialFactorials and divisionFactoring polynomialsFagnano's problem Fagnano's Problem, Third SolutionFagnano's Problem in ReverseL. Fejer's SolutionFair Division Method fo Lone DividerMethod of MarkersMethod of Sealed BidsFallacyFarey SeriesFeasible vectorsFechner ColorsFermat's Little TheoremFermat NumbersFermat Point and Generalizations Fermat-Torricelli PointFermat's PointFeuerbach's PointFeuerbach's TheoremFibonacci sequence Ceva's Theorem and Fibonacci BamboozlementFibonacci NimFibonacci NumbersFieldFifteen, the puzzle ofFifth PostulateFinite Cover PropertyFinite Intersection Property Infinity in CompactificationFinsler-Hadwiger theoremFirst Napoleon PointFirst Theorem of ApolloniusFish Soup GameFive Incircles TheoremFixed point About a Line and a TriangleFlank (triangle)Flipping pancakesFloorFocal ChordFocal DistanceFocal ParameterFocal RadiusFocus of a Conic Foci of an EllipseFoldingFord's touching circlesFormal FrameworkFour 3sFour 4sFour 5sFour Geometric Problems of AntiquityFourth ProportionalFractalFraction GameFractional partFree groupFree VariableFriendly Kiepert's PerspectorsFriendshipFriendship TheoremFrieze PatternsFrogs and ToadsFrogs and Toads in 2 dimensionsFulcrumFull angleFunctionFunction spacesFunctional equationFundamental Theorem of 3-Bar MotionFundamental Theorem of AlgebraFundamental Theorem of Arithmetic Almost Integers, Fundamental Theorem of ArithmeticFundamental Theorem of Directly Similar FiguresFunny ArithmeticFuss' TheoremGGalois ExtensionsGame of HexGame TheoryGauss-Bodenmiller theoremGaussian coordinatesGaussian IntegersGelfond's theorem, Gelgond-Schneider theoremGeneral Equation of a Straight LineGeneral position, lines inGeneralization in MathematicsGenerating FunctionGenetic AlgorithmsGeoboard, Toying with theGeometric ConstructionsGeometric mean Arithmetic-Geometric Mean InequalityGeometric series Sum of the geometric seriesGerbino's IllusionGergonne and Van Obel TheoremsGergonne LineGergonne PointGergonne TriangleGergonne's Magic TrickGibbs, Josiah WillardGion Shrine ProblemGirth of a GraphGLaD ConstructionGlide ReflectionGliderGnomonGödel's Incompleteness TheoremGolden rectangleGolden section Golden Ratio in GeometryGolden triangleGoogolGordius, King of PhrygiaGradientGraphGraph TheoryGray codesGreatest Common Divisor (gcd)Grebe's theoremGreedy algorithmGriffiths' theoremGroupGroupoidGrowthGrundy numberGrundy's GameGuest bookHHadwiger-Finsler InequalityHalf-axisHalf-turnHamilton CycleHamilton PathHamilton's Method of ApportionmentHamilton's theoremHamming DistanceHandshake LemmaHanoi, Tower ofHappy 8 puzzleHarmonic bundleHarmonic conjugatesHarmonic Mean Harmonic meanHarmonic RatioHarmonic SeriesHarmonic TriangleHart CircleHart's InversorHart's TheoremHaruki's LemmaHaruki's TheoremHausdorff DistanceHeaviside Step FunctionHeight in a triangle, formula forHering IllusionHeptadecagonHeptagonHeredityHering IllusionHermann Grid IllusionHeron's Formula DerivationHeron's ProblemHex Can't End in a DrawHex numbersHilbert's Plane Filling CurveHjelmslev TheoremHofstadter Triangles and PointsHoleHomogeneous CoordinatesHomogeneous FunctionsHomologousHomothety HomothetyHooked Langford SequenceHooper's ParadoxHopf FibrationHorner's MethodHour glass timingHow to define a permutation?Human calculatorsHummer's Mind ReaderHuntington-Hill's Method of ApportionmentHuzita's axioms of paper foldingHyperbinary expansionHypercubeHyperintegers and Hyperreal NumbersHypocycloidsIIan McGee's ObservationIdeal elementsIdeal subringsIdempotent lawIdentical Twins PuzzleIdentical TransformationIdentityIdentity matrixiffIllusory contourImaginary numbersImaginary Part of a Complex NumberImpartial gameA second lookImplicationImplicit Equation of a Straight LineImpossible ForkImpossible pageImproper IsometryIncidence matrixIncident points and linesIncenterIncenters in Cyclic QuadrilateralIncircleInclusion-Exclusion Principle Marriage TheoremIncompatible EventsIndegreeIndependent EventsIndexIndex Lemma, theInductionMathematical Induction: examplesInfinite Discent for x4 + y4 = z4Infinite Products ConvergentDivergentConvergent to 0Divergent to 0Infinite SumsInfinitesimalInfinitude of PrimesInfinity Infinity and ProbabilityWhat Is Infinity?Inflectin pointInjective functionInner productInner Soddy circleInradiusInscribed AnglesInscriptable (inscriptible) PolygonsIntegerInteger Iterations on a CircleIntegral DomainIntegration in Spherical CoordinatesInterceptIntercepted ArcInterest CalculationsInterior Angles formed by a secant and parallel linesIntermediate Value TheoremInternal pointInternal Tangent to Two CirclesInternet News sitesIntersecting Chords (Secants) Theorem Intersecting Chords TheoremIntersection of setsIntouch TriangleInvariant SetInventor's ParadoxInverse ElementInversion (combinatorial)Inversion (geometric) Inverse imageInversionInversion ToolInversion with Negative PowerInvert the Divisor and MultiplyInvolutionIrrational numbersISBN EncodingIsogonal lines Isogonal circleIsogonal conjugatesIsogonal ConjugalityIsogonal ConcurrencyIsogonic CentersIsolated pointIsometry Plane IsometriesIsosceles trapezoidIsosceles TetrahedronIsosceles triangleIsotomic linesIsotomic conjugatesIsoperimetric InequalityIsoperimetric TheoremIsoperimetric Theorem, a variation onIsoperimetric Theorem, a different oneIterative processJJamJapanese Theorem IJapanese Theorem IIJefferson's Method of ApportionmentJoachimsthal's NotationsJohn Sharp's ParadoxJohnson-Trotter MethodJordan Curve TheoremJosephus Flavius, a legend and a problemJudd IllusionJulia setsJumpKKanizsa TriangleKantor's CircleKaprekar's constantKaprekar's processKayles Grundy function for KaylesKiepert's TheoremKiepert's PerspectorKirkman's Theorem Pascal Lines: Steiner and Kirkman Theorems IIKitaoka's wavesKiteKlein BottleKnotsKoch's snowflakeKoffka's IllusionKönigsbergKönigsberg BridgesKronecker's symbolKruskal's algorithmKurschak's Tile and TheoremLLa Hire's Theorem La Hire's Theorem, a VariantJoachimsthal's NotationsLabeling of a graphLagrange's identity Lagrange's identity, ProofLagrange's polynomialLambert's TheoremLangford SequenceLangman's ParadoxLatin SquaresLatticeLatticeLattice MultiplicationLatus RectumLaw of CosinesLaw of excluded middleLaw of SinesLa Hire's TheoremLeafLeap YearLeast Common Multiple (lcm) Algorithm for Computing LCMLeft-handednessLeibniz TriangleLegendre's LemmaLemoine antiparallelLemoine circlesLemoine hexagonLemoine lineLemoine pointLéon Anne's theoremLeonardo's ClawsThe Lepidoptera of the CirclesThe Lepidoptera of the QuadrilateralLevel CurveLevenshtein DistanceLewis Carroll's problemLewis Carroll's Game of LogicLexicographic order Complex numbersPermutationsPigeonholeLights OutLindemann's TheoremLine at infinity Line at InfinityLine at infinityLinear combinationLinear functionLinear orderLinear ProgrammingLinear SpaceLinear TransformationLines in general positionLiouville's TheoremListing all permutationsLocal-Global PrincipleLocusLogarithmic spiralLogistic equationLogistic modelLogo of mineLone Divider MethodLong MultiplicationLong Runs of Composite NumbersLooking your bestLoopLooping ChipsLowest Terms, fraction inLoyd's Puzzles, Sam Can you better Sam Loyd?Farmer and Wife To Catch Rooster and HenSam Loyd's fifteenSam Loyd's Geometric PuzzlePlato's Geometric Numbers: can you better Sam Loyd?Puzzlist vs. Mathematician: A Practical Arithmetic ProblemThe Gordian KnotLubell-Yamamoto-Meshalkin inequalityLucas' Theorem Lucas' TheoremLucky 7 puzzle.LuneLYM inequalityMMaclaurin seriesMacLaurin's Construction of ConicsMagic in SquareMagic Squares gameMahavira's theoremMajor circle of ellipseMalfatti's ProblemMaltitudeMandelbrot and Julia sets Iterations and the Mandelbrot SetMannheim's TheoremManifestoMarkers Method of Fair DivisionMarriage TheoremMascheroni constructionsMasterMind, Invitation toMaterial PointMathematical ExpectationMatrixA Matter of AgeMaximal ChainMaximum Modulus TheoremMaxwell's TheoremMazes MazesMean ProportionalMean Value Theorem Rolle's and Mean Value TheoremsMechanical Proof of the Pythagorean TheoremMedial triangleMedian triangleMedianMedian PointMedians in a QuadrilateralMediant fraction Mediant fractionDots and FractionsMendelsohn tripleMenelaus Theorem Menelaus is equivalent to Ceva IMenelaus is equivalent to Ceva IIMerlin's Magic SquaresMetamathematicsMetric CompletenessMetric FunctionMetric SpaceMex rule Mex ruleMidline (in a triangle)MillipedeMini Lights OutMinimal LatticeMinimal-change PropertyMinimax PrincipleMinimax TheoremMinimum element in a posetMinimum Spanning Tree Minimum Spanning TreeMinkowski additionMinkowski subtractionMiquel's Point Miquel's Point of a 4-lineMiquel's Point of a 4-line Via Spiral SimilarityMirror property of the orthic triangleMirror property of the altitudesMixed Product of Three VectorsMixtilinear Circles and Concurrence Radius and Construction of a Mixtilinear CircleMobile IntegerModelModulo Arithmetic Modular ArithmeticModulus of a complex numberModus ponensModus tollensMöbius StripMöbius Transformations Möbius TransformationsMohr-Mascheroni constructionMonge PointMonge's Circle Theorem Monge via DesarguesMonge via Desargues IIMonic polynomialMonominoMonotone Convergence TheoremMonty Hall DilemmaMoore's Plane Filling CurveMorley's Miracle Doodling and MiraclesMost likely number of successes in Bernoulli trialsMüller-Lyer IllusionMost elementary theorem of Euclidean geometryMultiplicandMultiplicationMultiplicative InverseMultisetMutationMutually Exclusive EventsMutually prime integersMy logoN9-Point Center9-Point Circle 9-point Circle as a Locus of ConcurrencyNagel LineNagel Point Nagel PointNagel's TheoremNapier BonesNapoleon PointsNapoleon's Theorem Napoleon's Theorem, a generalizationNapoleon's Theorem by Plane TesselationNapoleon's Theorem, two proofsNapoleon's Theorem, complex variablesNapoleon's Theorem, circle incidenceNapoleon's PropellerNearNecker CubeNegative PowersNeighborhoodNephroidNested RadicalsNeuberg's Theorem Neuberg's Theorem, Synthetic proofNeusis Constructions NeusisNew-States ParadoxNewton-Gauss lineNewton's lineNewton's TheoremNim, the game ofNimbleNimberNim-heapNim-sumNine-point CircleNine dots problemn-Line Characteristic Constants of the n-LineNobbs' pointsNon-degenerate conicNon-Eclidean GeometriesNonseparable GraphNorm (of a vector)Normal playNormal topological spaceNorthcott's gameNothing is somethingNowhere dense setN-positionNumber LineNumber MosaicsNumber System With Base 36Numbers, types of Numbers, Conway's definitionNumeralNumeratorO1-1 correspondenceObtuse angle Obtuse angleObtuse triangleOdd permutationOdd vertexOddball ProblemOld Japanese TheoremOlof Hanner's Jigsaw PuzzleOne PileOne-sided surfacesOpen intervalOpen setsOpen walkOperations on FractionsOperatorOppositely Congruent FiguresOptical IllusionOptical Property of EllipseOrbison IllusionOrbitsOrder, Ordered SpaceOrdinary Generating FunctionOrdinateOrientationOrigamiOrthic AxisOrthic triangle Mirror property of the orthic triangleOrthocenterOrthocentric systemOrthodiagonal Quadrilateral Orthodiagonal QuadrilateralOrthogonal latin squaresOrthogonalityOrthologic TrianglesOrthopoleOther math sitesOutdegreeOuter Soddy circlePp-adic Expansionsp-adic NumbersPacePacking shapes in a planePalindromicPaper FoldingPaper strip activitiesPappus' Generalization of Euclid I.47Pappus' Theorem Dual to Pappus' TheoremParabola Parabola as locusParabolic MirrorParabola as EnvelopeParadoxParadox of Tristram ShandyParahexagonParallel LinesParallel PostulateParallelogramParallelogram Law Parallelogram lawParallelogram ruleParametric Equation of a Straight LineParity Parity of a node on a graphParpolygonParrondo ParadoxPartial order Partial order in a latticePartition of point sets in a planePartitioning a CirclePartizan gameA second lookPascal's IdentityPascal's linePascal Lines: Steiner and Kirkman TheoremsPascal's theorem Pascal's theoremPascal's Theorem, Homogeneous CoordinatesPascal in a Cyclic QuadrilateralPascal in EllipsePascal Triangle and Sierpinski Gasket Pascal Triangle and the Tower of HanoiPeano axiomsPeano CurvesPeano and Wunderlich's Plane Filling CurvesPeasant MultiplicationPeaucellier LinkagePedal circlePedal curvePedal pointPedal trianglePedal Construction of ParabolaPedal CurvePedoe's TheoremPeg Solitaire Peg Solitaire and Group TheoryPencil of circlesPencil of lines Munching on Inscribed AnglesPenosculantPentagon, construction ofPercentPerfect Langford SequencePerfect numberPerimeter SplitterPeriodic cyclePeriodic patterns in sin(N)Permutation How to define a permutationListing all permutationsWhat, how, and the WebPerpendicular bisectorPerspective triangles Triangles perspective from a pointTriangles perspective from a linePetersen Graphp Determination of pPick's TheoremPigeonhole principle Pigeonhole Principle and ExtensionsPitot's TheoremPivot TheoremPivotal PlayerPlace ValuePlainimPlainim MisèrePlanar graphPlanar polygonPlane Filling CurvesPlato's Geometric Numbers: can you better Sam Loyd?Plane IsometryPlücker's LinesPlus or MinusPoggendorff IllusionPoggendorff Illusion II Circular Poggendorff IllusionPointPoint at infinity Point at InfinityPoint at InfinityPoint at infinityPoint CirclePoint in a SquarePoint inside a trianglePoint-Slope Equation of a Straight LinePolar CirclePolar coordinatesPolar Equation of conicsPole and Polar with respect to an anglePole and Polar with respect to a circlePole and Polar with respect to a trianglePolePoles and PolarsPolygonPolygonal numberPolyominoPompeiu's Triangle and TheoremPoncelet's PorismPoncelet's TheoremPonzo IllusionPonzo Illusion IIPopulation ParadoxPorismPosetPositional Number SystemPositive (Counterclockwise) DirectionPower of a point with respect to a circle Power of a point with respect to a circlePower of InversionP-positionPredicatePrim's algorithmPrimePrime Number DecompositionPrimorialPrincipalPrinciple of Conservation of Angular MomentumPrinciple of DualityPrinciple of ProportionalityPrisoner's DilemmaProbability Probability density functionProbability distribution functionProbability paradoxesProduct of RotationsSequential RuleProizvolov's IdentityProjectionProjective GeometryProjective PlanePronkProofs Without Words ProofProper IsometryProperty of anPropositional VariableProtractor PostulatePtolemy's InequalityPtolemy's Theorem Ptolemy's Second TheoremPtolemy's Theorem implies Pythagoras' TheoremSine, Cosine, and Ptolemy's TheoremEuler's Generalization of Ptolemy's TheoremPure existence proofPurely Imaginary Complex Numberspuz(G), the graph of a puzzlePuzzles on graphsPythagoras' Theorem Mechanical Proof of the Pythagorean Theorem"Extra-geometric" proofs of the Pythagorean TheoremPythagorean Theorem, Generalizations ofPythagorean triples Proof of the formulaNorm of Gaussian integersGaussian integersDivisibilty in Pythagorean TriplesTrinary Tree(s) underlying Primitive Pythagorean TriplesQ Quadratic AverageQuadratic FieldQuadratic Formula Completing a Square and Quadratic FormulaQuadratic FunctionQuadrangleQuadrilateralQuarter-turnQuasigroup 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Rolle's and Mean Value TheoremsRotocenterRottary gallopRounding numbersRouse Ball's FallacyRouth's TheoremRow vectorRussell's ParadoxRussian Peasant MultiplicationRusty Compass Construction of Equilateral TriangleS7 Coins PuzzleSam Loyd's Puzzles Can you better Sam Loyd?Farmer and Wife To Catch Rooster and HenSam Loyd's fifteenSam Loyd's Geometric PuzzlePlato's Geometric Numbers: can you better Sam Loyd?Puzzlist vs. Mathematician: A Practical Arithmetic ProblemThe Gordian KnotSaddle PointSalinon: From Archimedes' Book of LemmasSalmon's pointsSam Loyd's fifteenSam Loyd's Geometric PuzzleSam Loyd's Son's DissectionSangakuSaRD ConstructionSASSawayama's LemmaScalarScalar productScalene triangleSchlafli formulaScintillating Grid IllusionScoringScoring MisèreScrub Tile PuzzleSealed Bids MethodSecant SecantSecant AnglesSecond Napoleon PointSecond Theorem of ApolloniusSector (in circle)See-Saw LemmaSegment (in circle)Self-conjugate triangleSelf-descriptive StringsSelf-documenting sentencesSelf-dual configurationSelf-referenceSemigroupSending scouts into the desertSeparating point sets with a circleSequential CoalitionSequential compactnessSequential RuleSetSeven Circles TheoremSeven Terms Periodic SequenceShaggy Dog TheoremShape PropertyShapes in a latticeShapes of constant width Star Construction of Shapes of Constant WidthShapley-Shubik IndexShearing TransformShepard's Parallelogram IllusionShiftShimmer IllusionShip-Dock TheoremShredding the torusShuttle PuzzleSibling nodeSierpinski CarpetSierpinski gasket Dot Patterns and Sierpinski GasketSierpinski Gasket by Trema RemovalSieve of Eratosthenesσ-AlgebraSigned segmentSignum function, sign(t)Silver Dollar GameSimilar orderingsSimilar Triangles, theorem ofSimilaritySimilarity dimensionSimple continued fractionSimple graphSimple polygonSimplexSimson Line Simson Line From Isogonal PerspectiveSimson-Wallace TheoremSimpson's paradoxSimultaneous Contrast IllusionSimultaneous Contrast Illusion IISine LawSingle formula to express any integer with digits 0-9 each used just onceSix Circles Theorem (Elkies)Six Circles Theorem (Evelyn)Skolem SequenceSlider PuzzlesSlidersSlopeSlope-Intercept Equation of a Straight LineSocial ChoiceSoddy circlesSoddy LineSoddy pointsSolitaire in the CircleSomos-4 SequenceSoritesesSorobanSorting AlgorithmsSpanning TreeSperner's LabelingSperner's LemmaSperner's TheoremSphereSpieker CenterSpira MirabilisSpiral Similarity Miquel's Point of a 4-line Via Spiral SimilaritySplitterSplitting pilesSprague-Grundy functionSquareSquare numbersSquaring a circleSquaring ParabolaSquares and CirclesSquares, Circles, and TrianglesSquinting Eyes TheoremSSSStabilityStaircase IllusionStar PolygonsStar-shaped regionStationary pointSteiner Porism Steiner PorismSteiner's CircleSteiner's CurveSteiner's TheoremSteiner's and Kirkman's Theorems Pascal Lines: Steiner and Kirkman Theorems IISteinhaus' ProblemStereographic projection Stereographic Projection and Radical AxesStern-Brocot Tree Binary Encoding with the Stern-Brocot treeStern's diatomic seriesStewart's theoremStraight angleStraight Edge Only Construction of Polar w.r.t. an AngleStraight Edge Only Construction of Polar w.r.t. a CircleStraight lineStraight TrominoStrategy stealing in the game of HexStretchingSuan panSubfactorialSubgraphSubgroupSubjective contourSubtraction GameSuccessorSum RuleSums and ProductsSuperfactorialSupergraphSuperposition PrincipleSupplementary anglesSupporting lines of convex figuresSurjective functionSurreal numbers Surreal NumbersSurreal numbers and gamesSyllogism, Modes Ponens Syllogism, more generalSymmedianSymmedian pointSymmetric differenceSymmetric groupSymmetric relationSymmetry in circleSynthetic divisionSystem of Distinct RepresentativesT3-4-5 triangle3 glass puzzle3 glass puzzle, second, more general toolT-JunctionTake-Away GamesTangent PairTangent to two circlesCircle of SimilitudeTangential triangleTarski-Banach DecompositionsTaylor circleTaylor seriesTelescoping SeriesTernary number systemTessellationTesseractThales' TheoremThales' TheoremThe only rational triangleThe Two Men of Tibet ProblemThébault's Problem IThébault's Problem IIThébault's Problem IIITheorem of Complete QuadrilateralTheorem of TheaetetusThick setThin setThird ProportionalThree pancakes problemThree 3sThree 4sThree 5sThree Circles and Common TangentsThree circles problemThree Tangents TheoremThree Tangents TheoremToads And Frogs PuzzleToothpick Construction of a SquareTopological equivalenceTopological SpaceTopological transformationTopologyTorqueTorricelli point">TorusTotality (of a binary relation)Totally ordered setTower of HanoiSierpinski Gasket and Tower of HanoiBicolor Towers of HanoiToys and Tots problemTrachoidsTrain wheel quandaryTranscendental numbersTransfinite CardinalityTransitive groupsTransitivity in ActionTransivityTranslation TransformTranspose of a vectorTranspositionWhat, how, and the WebTransversalTransverse gallopTrapezoidTreeTrefoil knotTremaTriangle ClassificationTriangle Inequality, theAxioms of distance functionAbsolute Value of Complex NumberTriangle of SimilitudeTriangular BilliardTriangular numbersThere exist triangular numbers that are also squareTriangulationDiagonal TriangulationTrichotomy, the law ofTrigonometric Form of Ceva's TheoremTrigonometric Form of Complex NumbersTrilateral DiagramsTrilinear CoordinatesTrivial Ramsey NumberTrominoStraight TrominoTrotTucker CirclesTurnTurning TurtlesTweedledum & Tweedledee PrincipleTwin Circles of ArchimedesTwisted Cord IllusionTwo Butterflies TheoremTwo Butterflies Theorem IITwo coins puzzleTwo Envelopes ParadoxTwo Numbers Guessing GameTwo-squares identityUUniform convergenceUniform probability distributionUnion of setsUnique Factorization TheoremUniqueness of number 30Unit elementUnit FractionUnityUniversal QuantifierUPC-A encodingUrquhart's Theorem Urquhart's TheoremV ValueVan Obel Theorem, Determinants, and Barycentric Coordinates Gergonne and Van Obel TheoremsVan Aubel's theoremVan Schooten's theorem Van Schooten's and Pompeiu's TheoremsVarignon ParallelogramVecten's CollinearityVecten configurationVecten PointsVectorVector productVector SpaceVenn DiagramsVergingVersineVertexVertical AnglesVi�te's FormulasViewing a StatueViviani's TheoremW Walk on a graphWallace-Bolyai-Gerwien TheoremWallace's TheoremWasanWeb pollWebster's Method of ApportionmentWeierstrass-Bolzano propertyWeierstrass Product InequalityWeighted graphWeird curves bound normal areasWeitzenböck InequalityWell-ordered setWhat do you call a centipede?White's IllusionWhole numberWhole part function, [x]Wilson's TheoremWittenbauer's ParallelogramWord LaddersWord ProblemsWunderlich's Plane Filling CurvesWundt IllusionWundt Block IllusionWythoff's NimWythoff's Nim IIX XORX-interceptY Y Can't End in a DrawY-interceptY. Sawayama's LemmaYosanZ 0!=1Zaslavsky's theoremZeckendorf's theoremZenodorus TheoremZeroZipf's LawZöllner's Illusion
What are the type of logic?
modus ponens and modus tollens
What is modus ponens?
Modus Ponens is very simple. lets say you have this example If today is Monday, then tomorrow is Tuesday. Today is Monday Therefore tomorrow is Tuesday. That is a valid argument because of modus ponens If the premise(if today is monday) is true then you must accept the conclusion(Then Tommorow is Tuesday) as true also. Another example If P, then Q P Therefore Q
How do you write an argument using modus ponens and modus tollens?
If today is MONDAY then tomorrow is Tuesday.
What has the author Horst Lange written?
Horst Lange has written: 'Kants modus ponens' -- subject(s): Metaphysics 'Ulanenpatrouille' 'Eine Geliebte aus Luft'
What is modus ponens in philosophy?
It is a valid argument form in which: If X, then Y. X. Therefore, Y. Example: If my dog is old, he will die soon. My dog is old. Therefore, he will die soon.
What is the proof of the modus ponens not by the truth table?
1)p->q 2)not p or q 3)p 4)not p and p or q 5)contrudiction or q 6)q
What is disjunctive syllogism in philosophy?
It is a valid argument form, also known as modus tollendos ponens, in which: Either X or Y. Not X. Therefore, Y. Example: Either I play the violin or the piano. I do not play the violin. Therefore, I play the piano.
What are some examples of particular terms in logic?
Some terms in logic are:axiom - something that is self-evident.deductive reasoning - the truth of the premises assures the truth of the conclusion, and the falsity of it is impossible.inductive reasoning - the premises support the conclusion, but do not necessitate it.fallacy - an argument that is based on an invialid or false inference.symbolic logic - representing expressions through the use of symbols and variable, rather than in ordinary language.contingency - a statement that might be true or false
Law of detachment?
Law of Detachment also known as Modus Ponens (MP) says that if p=>q is true and p is true, then q must be true. The Law of Syllogism is also called the Law of Transitivity and states: if p=>q and q=>r are both true, then p=>r is true.
Derive using inference given conclusion if g then c premise one if g or h then s and t premise two if t or u then c and d?
g => (g or h) => (s and t) => t => (t or u) => (c and d) => c.We are given premises:# (g or h) -> (s and t) # (t or u) -> (c and d) We would like to derive g -> c.If we assume g (the antecedent in the conclusion) we have the following derivation: # g (assumption) # g or h(weakening) # s and t (premise 1 (modus ponens)) # t(weakening) # t or u (weakening) # c and d (premise 2 (modus ponens)) # c (weakening)So, assuming g we can derive c, i.e. g -> c
Madeline must have known the material for the test because if a person knows the material that person will get an A and Madeline was one of the students that got an A?
this is a valid argument, affirming the antecedent, or a modus ponens. The structure is: If a person knows the material for the test, he/whe will get an A. (If P, then Q.) Madeline knew the material for the test, therefore she got an A. (P, therefore Q.)
What is the Law of detachment?
AnswerLaw of Detachment ( also known as Modus Ponens (MP) ) says that if p=>q is true and p is true, then q must be true.example:If an angle is obtuse, then it cannot be acute.Angle A is obtuse.ThereforeAngle A cannot be acute.The Law of Syllogism ( also called the Law of Transitivity ) states:if p=>q and q=>r are both true, then p=>r is true.example:If the electric power is cut, then the refrigerator does not work.If the refrigerator does not work, then the food is spoiled.So if the electric power is cut, then the food is spoiled.Law of Detachment also known as Modus Ponens (MP) says that if p=>q is true and p is true, then q must be true.The Law of Syllogism is also called the Law of Transitivity and states: if p=>q and q=>r are both true, then p=>r is true.In a nutshell, it's saying that if you have a conditional, and you have the antecedent, you then have the consequent. For example, we know that, "If it snows this winter, we will need to wear warm winter clothing outside." Suddenly it's mid-December and the forecast is snow. Therefore, it's probably the time to go shopping for winter clothes, if we don't already have any.
