First slide

Introduction to mathematical reasoning

Question

The negation of the compound proposition is $p \lor (~ p \lor q)$

Easy

A

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

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

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

None of these

Solution

$\begin{array}{l} since, S :\sim (p \lor (~ p \lor q)) \\ \Rightarrow S : ~ p \land ~ (~ p \lor q) (De-Morgan's Law) \\ \Rightarrow S : ~ p \land (p \land ~ q) (De-Morgan's law) \end{array}$

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