Question
$A\ B$
$\therefore B\ \&\ A$
$\therefore B\ \&\ A$
| Support Statement | The resulting statement | ||||
| $1$ | $2$ | $3$ | $4$ | ||
| $A$ | $B$ | $A\ \&\ B$ | $B\ \&\ A$ | ||
| $1$ | $T$ | $T$ | $T^*$ | $T^*$ | |
| $2$ | $T$ | $F$ | $F$ | $F$ | |
| $3$ | $F$ | $T$ | $F$ | $F$ | |
| $4$ | $F$ | $F$ | $F$ | $F$ | |
| $1, 2 (\&)$ | $2, 1 (\&)$ | ||||
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| $(A \leftrightarrow B) \rightarrow (D \leftrightarrow E)$ |
| $(D \leftrightarrow E) \rightarrow\ \sim H$ |
| $\sim\ \sim H$ |
| $\sim (A \leftrightarrow B) \rightarrow F$ |
| $(F\ v\ G)\ \&\ \sim\ \sim H$ |
| $M \rightarrow \sim (S \ \&\ T)$ |
| $\sim (A \ \&\ B)\ v\ \sim D$ |
| $\sim D (S \ \&\ T)$ |
| $M$ |
| $[\sim (A \ \&\ B) \ \&\ M)\ v\ D$ |
| $(A\ v\ B) \rightarrow D$ |
| $A$ |
| $\therefore (D\ \&\ A)\ v\ P$ |
| $P \rightarrow Q$ |
| $R \rightarrow S$ |
| $( \sim\ Q\ \&\ A) \& (P\ v\ R)$ |
| $\therefore (S\ v\ Z) \& \sim\ Q$ |
| $R \rightarrow S$ |
| $P \rightarrow Q$ |
| $P\ v\ Q$ |
| $Q \rightarrow R$ |
| $\therefore (P \rightarrow R) \& (R\ v\ S)$ |
| $A \rightarrow J$ |
| $B \rightarrow R$ |
| $(A\ v\ B)\&\ \sim D$ |
| $J \rightarrow D$ |
| $\therefore (D\ v\ R)\ \&\ (B\ v\ K)$ |