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Which term best describes the statement given If p q and q r then p r below?
a syllogism
What is the answer to add q and p triple the result then divide r by s?
It is 3*(q + p)/(r + s)
How does each multiplication problem compare to its cooresponding division problem?
By inverting the numbers. For example, if:2 x 3 = 6 then: 6 / 3 = 2
What are the inference rules for functional dependency?
"The present list of 19 rules of inference constitutes a COMPLETE system of truth-functional logic, in the sense that it permits the construction of a formal proof of validity for ANY valid truth-functional argument." (FN1)The first nine rules of the list are rules of inference that "correspond to elementary argument forms whose validity is easily established by truth tables." (Id, page 351). The remaining ten rules are the Rules of Replacement, "which permits us to infer from any statement the result of replacing any component of that statement by any other statement logically equivalent to the component replaced." (Id, page 359).Here are the 19 Rules of Inference:1. Modus Ponens (M.P.)p qpq 2.Modus Tollens (M.T.)p q~q~p 3.Hypothetical Syllogism (H.S.)p qq rp r 4.Disjunctive Syllogism (D.S.)p v q~ pq 5. Constructive Dilemma (C.D.)(p q) . (r s)p v rq v s 6. Absorption (Abs.)p qp (p. q)7. Simplification (Simp.)p . qp 8. Conjunction (Conj.)pqp . q 9. Addition (Add.)pp v qAny of the following logically equivalent expressions can replace each other wherever they occur:10.De Morgan's Theorem (De M.) ~(p . q) (~p v ~q)~(p v q) (~p . ~q) 11. Commutation (Com.)(p v q) (q v p)(p . q) (q . p) 12. Association (Assoc.)[p v (q v r)] [(p v q) v r][p . (q . r)] [(p . q) . r] 13.Distribution (Dist) [p . (q v r)] [(p . q) v (p . r)][p v (q . r)] [(p v q) . (p v r)] 14.Double Negation (D.N.)p ~ ~p 15. Transposition (Trans.)(p q) (~q ~p) 16. Material Implication (M. Imp.)(p q) (~p v q) 17. Material Equivalence (M. Equiv.)(p q) [(p q) . (q p)](p q) [(p . q) v (~p . ~q)] 18. Exportation (Exp.)[(p . q) r] [p (q r)] 19. Tautology (Taut.) p (p v p)p (p . p)FN1: Introduction to Logic, Irving M. Copi and Carl Cohen, Prentice Hall, Eleventh Edition, 2001, page 361. The book contains the following footnote after this paragraph: "A method of proving this kind of completeness for a set of rules of inference can be found in I. M. Copi, Symbolic Logic, 5th Edition. (New York: Macmillian, 1979), chap 8, See also John A. Winnie, "The Completeness of Copi's System of Natural Deduction," Notre Dame Journal of Formal Logic 11 (July 1970), 379-382."
Can the product of two rational numbers be irrational?
No.Suppose a and b are two rational numbers.Then they can be written as follows: a = p/q, b = r/s where p, q, r and s are integers and q, s >0.Then a*b = (p*r)/(q*s).Using the properties of integers, p*r and q*s are integers and q*s is non-zero. So a*b can be expressed as a ratio of two integers and so the product is rational.
If p q and q r then p r. Converse statement B.A syllogism C.Contrapositive statement D.Inverse statement?
Converse: If p r then p q and q rContrapositive: If not p r then not (p q and q r) = If not p r then not p q or not q r Inverse: If not p q and q r then not p r = If not p q or not q r then not p r
If p q and q r what is the relationship between the values p and r?
Ifp < q and q < r, what is the relationship between the values p and r? ________________p
If P 50 of Q and Q 50 of R then P Q R?
If P is 50% of Q, this means that P is half the value of Q. Similarly, if Q is 50% of R, then Q is half the value of R. Therefore, P is 25% of R, as it is 50% of Q, which is itself 50% of R. Thus, we can conclude that P is less than both Q and R.
How do you add and subtract rational numbers?
A rational number is a number of the form p/q where p and q are integers and q > 0.If p/q and r/s are two rational numbers thenp/q + r/s = (p*s + q*r) / (q*r)andp/q - r/s = (p*s - q*r) / (q*r)The answers may need simplification.
P varies directly as q and inversely as r?
P=q/r* * * * *The correct answer is P = k*q/r where k is the constant of proportionality.
What is P and q implies not not p or r if and only if q?
The statement "P and Q implies not not P or R if and only if Q" can be expressed in logical terms as ( (P \land Q) \implies (\neg \neg P \lor R) \iff Q ). This can be simplified, as (\neg \neg P) is equivalent to (P), leading to ( (P \land Q) \implies (P \lor R) \iff Q ). The implication essentially states that if both (P) and (Q) are true, then either (P) or (R) must also hold true, and this equivalence holds true only if (Q) is true. The overall expression reflects a relationship between the truth values of (P), (Q), and (R).
How do you add similar proper fraction?
Two fractions are similar if they have the same denominator.So if p/r and q/r are two such fractions, then p/r + q/r = (p+q)/r.
Which term best describes the statement if p q and q r the p r?
The statement "if p, then q; and if q, then r; therefore, if p, then r" describes the logical reasoning known as the transitive property. More formally, it can be expressed in symbolic logic as "p → q, q → r, therefore p → r." This is a fundamental concept in logic that illustrates how relationships can be inferred through a chain of implications.
P and q represents r p q?
tan x
L is not as tall as P or R but is taller than S and Q Q being shorter than R S is shorter than R who is shorter than P who is taller than Q Who among P Q R and S is the shortest?
The answer is Q.
What are the rules for multiplying rational numbers?
p/q * r/s = (p*r)/(q*s)
Which term best describes the statement If p q and q r then p r?
The statement "If p implies q and q implies r, then p implies r" is best described as the transitive property of implications in logic. This principle is fundamental in propositional logic and can be expressed symbolically as ( (p \rightarrow q) \land (q \rightarrow r) \rightarrow (p \rightarrow r) ). It highlights how the relationship between propositions can be extended through a chain of implications.
