d. peqand (рлq)v(-рл-g)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
D part only plz.
Thankyou.

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)

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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