First slide

Introduction to mathematical reasoning

Question

The statement $(~ p \land q) \lor ~ q$ is

Easy

A

$p \lor q$
B

$p \land q$
C

$~ (p \lor q)$
D

$~ (p \land q)$

Solution

$\begin{aligned} (~ p \land q) \lor ~ q \equiv\sim q \lor (~ p \land q) (by Commutative law) \\ \equiv\sim q \lor (q \land q ~ p) (by Commutative law) \\ \equiv\sim q \lor q (~ q \lor ~ p) (by Distributive law) \\ \equiv\sim (q \land p) \equiv\sim (p \land q) \end{aligned}$

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