Question
Using truth tables, examine whether the statement pattern $(p \wedge q) \vee(p \wedge r)$ is a tautology, contradiction or contingency.

Answer

No of rows = 2n=23 =8
No. of columns = m+ n=3+3= 6

Pqr$p \wedge q$$p \wedge r$$\begin{aligned} & (p \wedge q) \vee(p \wedge \\ & r)\end{aligned}$
TTTTTT
TTFTFT
TFTFTT
TFFFFF
FTTFFF
FTFFFF
FFTFFF
FFFFFF

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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