Construct truth table method whether or contradictory it contingency, tautology Pa(~P0~9)

The atomic propositions are $P$ and $Q$. We also need $\sim P$.

This column will show the truth values for the expression $(\sim P \lor Q)$.

This column will show the truth values for the entire expression $P \land (\sim P \lor Q)$.

Truth Table:

The final column for $P \land (\sim P \lor Q)$ contains both 'T' (True) and 'F' (False) values.

• A tautology is an expression that is always true.
• A contradiction is an expression that is always false.
• A contingency is an expression that is neither a tautology nor a contradiction (i.e., its truth value depends on the truth values of its components).

Since the final column has a mix of 'T' and 'F' values, the expression is a contingency.

The expression $P \land (\sim P \lor Q)$ is a contingency.