Question
p → (p v ~ p)
| 1 | 2 | 3 | 4 | |
| p | ~ p | p v ~ p | p $\rightarrow$ (p v ~ p) | |
| 1 | T | F | T | T |
| 2 | F | T | T | T |
| 1(~) | 1, 2 (V) | 1, 3 ($\rightarrow$) | ||
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| $A \rightarrow B$ |
| $A\ v\ C$ |
| $E\ \&\ \sim F$ |
| $\sim B$ |
| $\therefore\ C\ \&\ \sim F$ |
| $(A\ \&\ B) \rightarrow\ \sim\ R$ |
| $R\ v\ \sim \ D$ |
| $T \rightarrow B$ |
| $D\ v\ (B \rightarrow P)$ |
| $A\ \&\ B$ |
| $\therefore (T\ P)\ v\ L$ |
| $A\ \rightarrow\ B$ |
| $(R\ \&\ D)\ v\ A$ |
| $T\ v\ [(R\ \&\ D)\ \rightarrow\ W]$ |
| $D\ \&\ \sim\ T$ |
| $\therefore\ [D\ \&\ (W\ v\ B)])\ v\ \sim\ A$ |
| (~ X v ~ Y) $\rightarrow$ [A $\rightarrow$ (P & ~ Q)] |
| (~ X & ~R) $\rightarrow$ [(P & ~Q) $\rightarrow$ Z) |
| (~ X & ~R) & (~ Z v A) |
| $\therefore$ (A $\rightarrow$ Z) v ~ R |