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
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
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)
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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