Mathematical Reasoning Question 2
Question 2 - 24 January - Shift 2
Let $p$ and $q$ be two statements.Then $\sim(p \wedge(p \Rightarrow \sim q))$ is equivalent to
(1) $p \vee(p \wedge(\sim q))$
(2) $p \vee((\sim p) \wedge q)$
(3) $(\sim p) \vee q$
(4) $p \vee(p \wedge q)$
Show Answer
Answer: (3)
Solution:
$\sim(p \wedge(p \to \sim q))$
$\equiv \sim p \vee \sim(\sim p \vee \sim q)$
$\equiv \sim p \vee(p \wedge q)$
$\equiv(\sim p \vee p) \wedge(\sim p \vee q)$
$\equiv t \wedge(\sim p \vee q)$
$\equiv \sim p \vee q$
