First slide

Introduction to mathematical reasoning

Question

$The Boolean Expression (p \land ~ q) \lor q \lor (~ p \land q) is equivalent to$

Moderate

A

$~ p \land q$
B

$p \land q$
C

$p \lor q$
D

$p \lor ~ q$

Solution

$Consider (p \land ~ q) \lor q \lor (~ p \land q)$
$= [(p \lor q) \land (~ q \lor q)] \lor (~ p \land q)$
$\begin{array}{l} = [(p \lor q)] \lor (~ p \land q) \\ = p \lor q \lor (~ p \land q) \\ = (p \lor q \lor p) \land (p \lor q \lor q) \\ = (p \lor q) \land (p \lor q) \\ = p \lor q \end{array}$

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