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5. Use the laws of propositional logic to prove that the following compound propositions are tautologies. а. ((р - 9) лр) — q b. ((p → q) ^ (¬p → r)) → (¬q → r)

5. Use the laws of propositional logic to prove that the following compound propositions are tautologies. а. ((р - 9) лр) — q b. ((p → q) ^ (¬p → r)) → (¬q → r)

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 10CT: Statement P and Q are true while R is a false statement. Classify as true or false:...
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Solve part B please

Idempotent laws p V p = p d = dy d (p ^ q) Ar = p ^ (q ^r) Associative laws ( φν) Vr=pV (q Vr . Commutative laws p V q = q V p p^ q = q ^p Distributive laws p V (q Ar) = (p V q) ^ (p V r) p^ (ą v r) = (p ^ q) v (p ^r) Identity laws pVF = p p^T = p Domination laws p V T = T p A F = F Double negation laws p קבר Complement (or negation) laws p V ¬p = T p^ ¬p = F De Morgan's laws ¬(p V q) = ¬p ^ ¬q ¬(p ^ q) = ¬p V ¬q Absorption laws pV (pΛq) p d = (b ^ d) v d Conditional identities p → q = -p V q реда(р-д) л (q — р)
Transcribed Image Text:Idempotent laws p V p = p d = dy d (p ^ q) Ar = p ^ (q ^r) Associative laws ( φν) Vr=pV (q Vr . Commutative laws p V q = q V p p^ q = q ^p Distributive laws p V (q Ar) = (p V q) ^ (p V r) p^ (ą v r) = (p ^ q) v (p ^r) Identity laws pVF = p p^T = p Domination laws p V T = T p A F = F Double negation laws p קבר Complement (or negation) laws p V ¬p = T p^ ¬p = F De Morgan's laws ¬(p V q) = ¬p ^ ¬q ¬(p ^ q) = ¬p V ¬q Absorption laws pV (pΛq) p d = (b ^ d) v d Conditional identities p → q = -p V q реда(р-д) л (q — р)
5. Use the laws of propositional logic to prove that the following compound propositions are tautologies. а. ((р - 9) лр) — q b. ((p → q) ^ (¬p → r)) → (¬q → r)
Transcribed Image Text:5. Use the laws of propositional logic to prove that the following compound propositions are tautologies. а. ((р - 9) лр) — q b. ((p → q) ^ (¬p → r)) → (¬q → r)
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