Q.Construct the truth table for $(p \vee q) \wedge \sim p$ and classify it as a tautology, contradiction or contingency.

Compute $p \vee q$ and $\sim p$, combine them with $\wedge$, and read the final column.

The pattern is true only when $p$ is false but $q$ is true.

There are $4$ rows. Build $p \vee q$, then $\sim p$, then their conjunction.

Reading the rows. The conjunction is true only when both $p \vee q$ and $\sim p$ are true. That needs $\sim p = T$ (so $p = F$) together with $p \vee q = T$ (so $q = T$) — only row 3. The final column is $F, F, T, F$.

Since it contains both $T$ and $F$, the pattern is a contingency.

Verification. The lone true row is $p = F, q = T$: there $p \vee q = T$ and $\sim p = T$, so the conjunction is $T$; every other row has either $p \vee q = F$ or $\sim p = F$, forcing $F$ — consistent with the column above.

Students sometimes stop after finding one true row and mislabel the pattern. Classification needs the whole column: one T and at least one F together mean contingency, not tautology or contradiction.