Question

The negation of the inverse of the statement \(\sim p∨\sim q\) is...

• A. \(p∧q\)
• B. \(\sim p∧q\)
• C. \(\sim p∧\sim q\)
• D. \(p∨q\)

Hint:

Read the statement as p implies not q, take its inverse, then negate.

Answer 1

The Correct Option is C

Step 1: Convert to a conditional:
$\sim p \lor \sim q \equiv p \to \sim q$.

Step 2: Inverse then simplify:
Inverse means negate both parts: $\sim p \to q$, which equals $\sim(\sim p) \lor q = p \lor q$.

Step 3: Negate:
The negation of $p \lor q$ is $\sim p \land \sim q$, using De Morgan.

Final Answer:
The answer is not p and not q, option (C). \[ \boxed{\sim p \wedge \sim q} \]