First slide

Introduction to mathematical reasoning

Question

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

Easy

A

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

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

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

None of these

Solution

$\begin{array}{lrl} Let S : (p \lor q) \land (p \lor ~ r) \\ \Rightarrow ~ S :\sim (p \lor q) \lor ~ (p \lor ~ r) \\ ∴ ~ S : (~ p \land ~ q) \lor (~ p \land r) \end{array}$

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