First slide

Introduction to mathematical reasoning

Question

$~ (p \lor (~ p \lor q))$ is equal to

Moderate

A

$~ p \land (p \land ~ q)$
B

$(p \land ~ q) \lor ~ p$
C

$(p \lor ~ q) \lor ~ p$
D

None of these

Solution

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

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