Answer
See below.
Work Step by Step
1. Based on the given conditions, we can convert each case as Boolean expressions:
a) (P^Q)v(~P∧Q)v(P^~Q)
b) P∨Q
2. Use Theorem 2.1.1, we have:
a) (P^Q)v(~P∧Q)v(P^~Q)≡((Q^P)v(Q∧~P))v(P^~Q)≡
Q^(Pv~P)v(P^~Q)≡Q^(t)v(P^~Q)≡Qv(P^~Q)≡
(QvP)^(Qv~Q)≡(PvQ)^t≡P∨Q
3. Thus we can conclude that a) and b) are equivalent.
