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)≡((P^Q)v(P∧~Q))v(∼P^~Q)≡
P^(Qv~Q)v(∼P^~Q)≡P^(t)v(∼P^~Q)≡Pv(∼P^~Q)≡
(Pv∼P)^(Pv~Q)≡t^(Pv~Q)≡P∨~Q
3. Thus we can conclude that a) and b) are equivalent.
