Question
p $\leftrightarrow$ [p v (q & ~ q)]
| 1 | 2 | 3 | 4 | 5 | 6 | |
| p | q | ~ q | q & ~ q | p v (q & ~ q)] | p $\leftrightarrow$ [p v (q & ~ q)] | |
| 1 | T | T | F | F | T | T |
| 2 | T | F | T | F | T | T |
| 3 | F | T | F | F | F | T |
| 4 | F | F | T | F | F | T |
| 2 (~) | 2, 3 (&) | 1,4 (v) | 1, 5 ($\leftrightarrow$) | |||
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| $(M \leftrightarrow N) \rightarrow O$ |
| $\sim A\ v\ (B\ \&\ D)$ |
| $B \rightarrow (O \rightarrow P)$ |
| $\sim \sim A$ |
| $\therefore (M \leftrightarrow N) \rightarrow P$ |
| $R \rightarrow S$ |
| $P \rightarrow Q$ |
| $P\ v\ Q$ |
| $Q \rightarrow R$ |
| $\therefore (P \rightarrow R) \& (R\ v\ S)$ |
| $(T\ \&\ P) \rightarrow \sim Q$ |
| $\sim (T\ \&\ P) \rightarrow (R \rightarrow \sim Q)$ |
| $(\sim S\ v\ R)\rightarrow\ \sim\ \sim Q$ |
| $\sim S$ |
| $\therefore \sim R\ \&\ \sim S$ |