Question

If $p$ and $q$ are two statements, then $(p \land q) \lor (q \leftrightarrow p)$ is

• A. tautology
• B. contradiction
• C. neither tautology nor contradiction
• D. either tautology or contradiction

Hint:

If expression varies with cases → neither tautology nor contradiction.

Answer 1

The Correct Option is C

Concept: Evaluate logical expression using truth table.

Step 1: Understand components.
\[ p \land q = \text{true only when both true} \] \[ q \leftrightarrow p = \text{true when both same} \]

Step 2: Check cases.
Expression is sometimes true and sometimes false.

Step 3: Conclusion from truth table.
Not always true (not tautology), not always false (not contradiction). Conclusion:
Answer = neither tautology nor contradiction