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Use the laws of propositional logic to prove that the following compound propositions are tautologies. a. (p^q) → (q V r) b. ((¬p → q) ^ (p → r) ^ (q → r)) →r 5.

Use the laws of propositional logic to prove that the following compound propositions are tautologies. a. (p^q) → (q V r) b. ((¬p → q) ^ (p → r) ^ (q → r)) →r 5.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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1. Idempotent laws pvp = p pap=p 2. Associative laws (p v q) vr = p v (q v r) (p^q)ar=p^ (q^r) 3. Commutative laws pvq = qvp pnq = qAp 4. Distributive laws pv (qAr) (φν)^ φVr) p^(q vr) = (p^q) v (p ^r) 5. Identity laws pVF = p pAT = p 6. Domination laws pVT =T pAF = F 7. Complement laws pV-p = T pA-p = F 8. Double negation law p= ץרה 9. De Morgan's laws ¬(p v q) = -p A ¬q ¬(p Aq) = -p V ¬4 10. Absorption laws pv (p^ q) = p p^ (p v q) = p 11. Conditional identities p- q = -p v q p+ q = (p → q) ^ (q → p)
Transcribed Image Text:1. Idempotent laws pvp = p pap=p 2. Associative laws (p v q) vr = p v (q v r) (p^q)ar=p^ (q^r) 3. Commutative laws pvq = qvp pnq = qAp 4. Distributive laws pv (qAr) (φν)^ φVr) p^(q vr) = (p^q) v (p ^r) 5. Identity laws pVF = p pAT = p 6. Domination laws pVT =T pAF = F 7. Complement laws pV-p = T pA-p = F 8. Double negation law p= ץרה 9. De Morgan's laws ¬(p v q) = -p A ¬q ¬(p Aq) = -p V ¬4 10. Absorption laws pv (p^ q) = p p^ (p v q) = p 11. Conditional identities p- q = -p v q p+ q = (p → q) ^ (q → p)
5. Use the laws of propositional logic to prove that the following compound propositions are tautologies. a. (p ^q) → (q Vr) b. ((-p → q) ^ (p → r) ^ (q → r)) → r
Transcribed Image Text:5. Use the laws of propositional logic to prove that the following compound propositions are tautologies. a. (p ^q) → (q Vr) b. ((-p → q) ^ (p → r) ^ (q → r)) → r
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