Answer
See below.
Work Step by Step
1. Based on the given conditions, we can convert each case as Boolean expressions:
a) $\sim(\sim P\wedge Q)\wedge \sim P$
b) $\sim(P\vee Q)$
2. Use Theorem 2.1.1, we have:
a) $\sim(\sim P\wedge Q)\wedge (\sim P)
\equiv \sim(\sim P)\vee\sim Q\wedge (\sim P)
\equiv (P\vee\sim Q)\wedge (\sim P)
\equiv (\sim P)\wedge (P\vee\sim Q)
\equiv (\sim P\wedge P)\vee (\sim P\wedge\sim Q)
\equiv (c)\vee (\sim P\wedge\sim Q)
\equiv \sim P\wedge\sim Q
\equiv \sim (P\vee Q)$
3. Thus we can conclude that a) and b) are equivalent.
