Question
$(p \leftrightarrow q)\ \&\ \sim (p \leftrightarrow q)$
| $1$ | $2$ | $3$ | $4$ | $5$ | |
| $p$ | $q$ | $p \leftrightarrow q$ | $\sim (p \leftrightarrow q)$ | $(p \leftrightarrow q)\ \&\ \sim (p \leftrightarrow q)$ | |
| $1$ | $T$ | $T$ | $T$ | $F$ | $F$ |
| $2$ | $T$ | $F$ | $F$ | $T$ | $F$ |
| $3$ | $F$ | $T$ | $F$ | $T$ | $F$ |
| $4$ | $F$ | $F$ | $T$ | $F$ | $F$ |
| $1, 2( \leftrightarrow )$ | $3(\sim )$ | $3, 4 (\&)$ | |||
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| $(J \rightarrow K)\ \&\ R$ |
| $\sim P \rightarrow (A \rightarrow B)$ |
| $P\ v\ (J\ v\ A)$ |
| $\sim P$ |
| $\therefore K\ v\ B$ |
| $A \rightarrow B$ |
| $D\ v\ A$ |
| $E\ \rightarrow \sim\ D$ |
| $F\ v\ E$ |
| $\therefore\ A\ \&\ B$ |
| $A\ v\ B$ |
| $\sim\ A\ \&\ C$ |
| $\therefore (B\ v\ \sim\ D)\ \&\ C$ |