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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| $M \rightarrow N$ |
| $N \rightarrow O$ |
| $(M \rightarrow O) \rightarrow (N \rightarrow P)$ |
| $(N \rightarrow P) \rightarrow Q$ |
| $(Q\ v\ Z)\ \&\ Q$ |
| $(A\ \rightarrow\ B)\ \&\ (D\ \rightarrow\ E)$ |
| $(B\ \rightarrow\ T)\ \&\ (E\ \rightarrow\ A)$ |
| $\sim\ T$ |
| $\therefore\ \sim\ D\ \&\ \sim\ T$ |
| $(P\ \&\ Q) \rightarrow R$ |
| $R \rightarrow (H \rightarrow G)$ |
| $H\ \&\ K$ |
| $P\ \&\ Q$ |
| $\therefore (G\ v\ I)\ \&\ H$ |
| $(P \leftrightarrow Q) \rightarrow (A \leftrightarrow B)$ |
| $(R \ \&\ S)\ v\ (P \leftrightarrow Q)$ |
| $(F \ \&\ D) \rightarrow \sim\ (R \ \&\ S)$ |
| $(H \ \&\ G)\ v\ (F \ \&\ D)$ |
| $\sim (H \ \&\ G)$ |
| $(A \leftrightarrow B)\ v\ (B \leftrightarrow D)$ |