First slide

Introduction to mathematical reasoning

Question

Which of the following is logically equivalent to $~ (~ p \to q) ?$

Moderate

A

$p \land q$
B

$p \land ~ q$
C

$~ p \land q$
D

$~ p \land ~ q$

Solution

We know that $p \to q \equiv\sim p \lor q$
$\begin{array}{l} ∴ ~ p \to q \equiv p \lor q \\ ∴ ~ (p \to q) \equiv\sim (p \lor q) \\ \equiv\sim p \land ~ q \end{array}$

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