Question
$A \rightarrow B$
$B$
$\therefore A$
$B$
$\therefore A$
| Support Statement | The resulting statement | |||||
| $1$ | $2$ | $3$ | $4$ | $5$ | ||
| $A$ | $B$ | $A \rightarrow B$ | $(A \rightarrow B) B$ | $A$ | ||
| $1$ | $T$ | $T$ | $T$ | $T$ | $T$ | |
| $2$ | $T$ | $F$ | $F$ | $F$ | $T$ | |
| $3$ | $F$ | $T$ | $T$ | $T^*$ | $F^*$ | |
| $4$ | $F$ | $F$ | $T$ | $F$ | $F^*$ | |
| $1, 2 (\rightarrow)$ | $3,2 (\&)$ | As $1$ | ||||
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| $A \rightarrow B$ |
| $B \rightarrow S$ |
| $A\ \&\ T$ |
| $\therefore S\ \&\ T$ |
| $A \rightarrow B$ |
| $\sim B\ v\ D$ |
| $\sim D$ |
| $\therefore \sim A\ \&\ \sim D$ |
| (A & B) $\rightarrow$ [A $\rightarrow$ (D & E)] |
| (A & B) & C |
| $\therefore$E v G |