First slide

Introduction to mathematical reasoning

Question

Contrapositive of $p \to (q \to r)$ is logically equivalent to

Easy

A

$p \to (q \to r)$
B

$(q \to r) \to\sim p$
C

$p \lor q \to r$
D

$(q \to r) \to p$

Solution

Contrapositive of $p \to (q \to r)$ is
$\begin{array}{l} ~ (q \to r) \to\sim p \\ \equiv ~ [~ (q \to r)] \lor (~ p) \\ \equiv (q \to r) \lor (~ p) \equiv (~ p) \lor (q \to r) \\ \equiv p \to (q \to r) \end{array}$

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