First slide

Introduction to mathematical reasoning

Question

The negation of $q \lor ~ (p \land r)$ is

Moderate

A

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

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

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

None of these

Solution

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

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