Mathematical Reasoning Question 3
Question 3 - 25 January - Shift 1
The statement $(p \wedge(\sim q)) \Rightarrow(p \Rightarrow(\sim q))$ is
(1) equivalent to $(\sim p) \vee(\sim q)$
(2) a tautology
(3) equivalent to $p \vee q$
(4) a contradiction
Show Answer
Answer: (2)
Solution:
$ \begin{aligned} & (p \wedge \sim q) \to(p \to \sim q) \\ & \equiv(\sim(p \wedge \sim q)) \vee(\sim p \vee \sim q) \\ & \equiv(\sim p \vee q) \vee(\sim p \vee \sim q) \\ & \equiv \sim p \vee t \equiv t \end{aligned} $
