Question
Construct the truth table of ‘$\rightarrow$’.
| Component statements and their truthfulness | Joint statement and its veracity | |
| p | q | p $\rightarrow$ q |
| T | T | T |
| T | F | F |
| F | T | T |
| F | F | T |
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| (1) (X $\rightarrow$ Y) $\rightarrow$ (A $\rightarrow$ B) | P |
| (2)(A $\rightarrow$ B) $\rightarrow$ R | P |
| (3) [(X $\rightarrow$ Y) $\rightarrow$ R] $\rightarrow$ K=J | P |
| (4) J $\rightarrow$ K | P/ $\therefore$ (J $\rightarrow$ K) & (J & K) |
| (5) ( X $\rightarrow$ Y) $\rightarrow$ R | ................ |
| (6) J | ................ |
| (7)K | ................ |
| (8) J & K | ................ |
| (9) (J $\rightarrow$ K) & (J &K) | ................ |
| (1) (J $\rightarrow$ K) & (L $\rightarrow$ M) | P |
| (2) J & L | P/ $\therefore$ K & M |
| (3) J $\rightarrow$ K | ................ |
| (4) J | ................ |
| (5) K | ................ |
| (6) L $\rightarrow$ M | ................ |
| (7) L | ................ |
| (8) M | ................ |
| (9) K & M | ................ |