Question

Let $p$ and $q$ be two statements Then $\sim(p \wedge(p \Rightarrow \sim q))$ is equivalent to

• A. $p \vee(p \wedge q)$
• B. $(\sim p) \vee q$
• C. $p \vee(p \wedge(\sim q))$
• D. $p \vee((\sim p) \wedge q)$

Answer 1

Answer: (B)

$(\sim p) \vee q$

Answer 2

The correct answer is (B) : $(\sim p) \vee q$
∼(p∧(p→∼q))
≡∼p∨∼(∼p∨∼q)
≡∼p∨(p∧q)
≡(∼p∨p)∧(∼p∨q)
≡t∧(∼p∨q)
≡∼p∨q