First slide

Introduction to mathematical reasoning

Question

$(~ (p \lor q)) \lor (~ p \land q$ is logically equivalent to

Moderate

A

$p$
B

$~ p$
C

$q$
D

$~ q$

Solution

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

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