First slide

Introduction to mathematical reasoning

Question

Negation of the statement $(p \land r) \to (r \lor q)$ is

Moderate

A

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

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

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

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

Solution

we know that $~ (p \to q) \equiv p \land ~ q$
$\begin{matrix} ∴ ~ ((p \land r) \to (r \lor q)) \equiv (p \land r) \land [~ (r \lor q)] \\ \equiv (p \land r) \land (~ r \land ~ q) \end{matrix}$

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