Question
Using truth tables, examine whether the statement pattern $(p \wedge q) \vee(p \wedge r)$ is a tautology, contradiction or contingency.
No of rows = 2n=23 =8
No. of columns = m+ n=3+3= 6
| P | q | r | $p \wedge q$ | $p \wedge r$ | $\begin{aligned} & (p \wedge q) \vee(p \wedge \\ & r)\end{aligned}$ |
| T | T | T | T | T | T |
| T | T | F | T | F | T |
| T | F | T | F | T | T |
| T | F | F | F | F | F |
| F | T | T | F | F | F |
| F | T | F | F | F | F |
| F | F | T | F | F | F |
| F | F | F | F | F | F |
In the last column, the truth values of the statement is neither all T nor all F. Hence, it is neither a tautology nor a contradiction i.e. it is a contingency.
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