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d. peqand (рлq)v(-рл-g)

d. peqand (рлq)v(-рл-g)

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)
Part II: Proving logical equivalence using laws of propositional logic 4. Use the laws of propositional logic to prove that the following compound propositions are logically equivalent. a. (pA¬q) V ¬(p V q) and ¬q b. -p → -(q v r) and (q → p) ^ (r → p) c. ¬(p v (¬q ^ (r → p))) and ¬p ^ (¬r → q) d. p+ q and (p ^ q) V (¬p ^ ¬q)
Transcribed Image Text:Part II: Proving logical equivalence using laws of propositional logic 4. Use the laws of propositional logic to prove that the following compound propositions are logically equivalent. a. (pA¬q) V ¬(p V q) and ¬q b. -p → -(q v r) and (q → p) ^ (r → p) c. ¬(p v (¬q ^ (r → p))) and ¬p ^ (¬r → q) d. p+ q and (p ^ q) V (¬p ^ ¬q)
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