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In propositional logic, if we have statements p, q, and r, and we know that p is false, q is false, and r is true, the overall truth of a compound statement involving these variables would depend on the specific logical connectors used (such as AND, OR, NOT). For example, if the statement is "p AND q AND r," the result would be false, as both p and q are false. However, if the statement is "p OR q OR r," the result would be true because r is true. Thus, the truth value of the overall statement cannot be determined without knowing its specific form.
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Examples of deductive reasoning in geometry?
Law of Syllogism If p->q and q->r are true conditionals, then p -> r is also true. (P)If people live in Manhattan, (q) then they live in New York. (q)If people live in New York, (r) then they live in the United States. Law of Detachment IF p-> q is a true conditional and p is true, then q is true. If you break an item in a store, you must pay for it. (P) Jill broke a vase in Potter's Gift Shop. (q) Jill must pay for the vase.
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.
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.
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.
If p q and q r then p r.?
Unfortunately, the browser used for posting questions is hopelessly inadequate for mathematics: it strips away most symbols. All that we can see is "If p q and q r then p r.?". There is no operator between the variables. Some operators are transitive, others are not. In the case of the operator "is not equal to", the answer is that it depends. In the case of "is the parent of" the answer is no.
This statement is false brain teaser?
Let us consider "This statement is false." This quotation could also be read as "This, which is a statement, is false," which could by extent be read as "This is a statement and it is false." Let's call this quotation P. The statement that P is a statement will be called Q. If S, then R and S equals R; therefore, if Q, then P equals not-P (since it equals Q and not-P). Since P cannot equal not-P, we know that Q is false. Since Q is false, P is not a statement. Since P says that it is a statement, which is false, P itself is false. Note that being false does not make P a statement; all things that are statements are true or false, but it is not necessarily true that all things that are true or false are statements. In summary: "this statement is false" is false because it says it's a statement but it isn't.
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).
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.
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
Examples of deductive reasoning in geometry?
Law of Syllogism If p->q and q->r are true conditionals, then p -> r is also true. (P)If people live in Manhattan, (q) then they live in New York. (q)If people live in New York, (r) then they live in the United States. Law of Detachment IF p-> q is a true conditional and p is true, then q is true. If you break an item in a store, you must pay for it. (P) Jill broke a vase in Potter's Gift Shop. (q) Jill must pay for the vase.
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.
What is the proof of transitivity in logic NOT with truth table if p is q and if r is s and either p or r is true therefore either q or s is true?
Prove: [ P -> Q AND R -> S AND (P OR R) ] -> (Q OR S) -> NOT, --- 1. P -> Q ___ hypothesis 2. R -> S ___ hypothesis 3. P OR R ___ hypothesis 4. ~P OR Q ___ implication from hyp 1. 5. ~R OR S ___ implication from hyp 2 6. ~P OR Q OR S ___ addition to 4. 7. ~R OR Q OR S ___ addition to 5. 8. Let T == (Q OR S) ___ substitution 9. (~P OR T) AND (~R OR T) ___ Conjunction 6,7 10. T OR (~P AND ~R) ___ Distribution from 9 11. T OR ~(P OR R) ___ De Morgan's theorem 12. Let M == (P OR R) ___ substitution 13. (T OR ~M) AND M ___ conjunction 11, hyp 3 From there, you can use distribution to get (T AND M) OR (~M AND M). The contradiction goes away leaving you with T AND M, which can simplify to T.
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.
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.
