First slide

Introduction to mathematical reasoning

Question

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

Easy

A

$p \land q$
B

$p \land ~ q$
C

$~ p \land q$
D

$~ p \land ~ q$

Solution

$\begin{matrix} ~ (~ p \to q) \equiv\sim ((~ (~ p)) \lor q) \\ \equiv\sim (p \lor q) \\ \equiv\sim p \land ~ q \end{matrix}$

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