Question

The negation of statement pattern $(p \wedge \sim q) \rightarrow (p \vee \sim q)$ is

• A. a tautology
• B. a contingency
• C. a contradiction
• D. equivalent to $p \vee q$

Hint:

$\sim(P \rightarrow Q) \equiv P \wedge \sim Q$. If you test this with a truth table, you will find all entries are False.

Answer 1

The Correct Option is C

Step 1: Simplify the Pattern
The statement is of the form $X \rightarrow Y$. We know that $p \wedge \sim q$ is a subset of $p \vee \sim q$. In logic, if the antecedent is true, the consequent is also true. Thus, $(p \wedge \sim q) \rightarrow (p \vee \sim q)$ is a tautology ($T$).

Step 2: Apply Negation
The question asks for the negation of the entire pattern.
$\sim [ (p \wedge \sim q) \rightarrow (p \vee \sim q) ] = \sim [ T ] = F$ (Contradiction).

Step 3: Conclusion
The negation of a tautology is always a contradiction.
Final Answer: (C)