Question

The statement pattern \[ [(p \vee q) \wedge \neg p] \wedge (\neg q) \] is

• A. a contradiction
• B. equivalent to \( p \wedge q \)
• C. a contingency
• D. a tautology

Hint:

A contradiction occurs when a logical expression simplifies to a falsehood. Always check for terms that cannot be true at the same time.

Answer 1

The Correct Option is A

Step 1: Simplifying the expression.
We are given the logical expression \( (p \vee q) \wedge \neg p \wedge \neg q \). First, we simplify the expression: \[ (p \vee q) \wedge \neg p = q \wedge \neg p \] Then we combine it with \( \neg q \): \[ q \wedge \neg p \wedge \neg q = 0 \] This is a contradiction because the same variable, \( q \), cannot be both true and false simultaneously.
Step 2: Conclusion.
Since the expression simplifies to a contradiction, the correct answer is option (A).