First slide

Introduction to mathematical reasoning

Question

The contrapositive of $(p \lor q) \to r$ is

Moderate

A

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

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

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

$p \to (q \lor r)$

Solution

Contrapositive of $p \to q is ~ q \to\sim p$
Therefore, contrapositive of $(p \lor q) \to r$ is
$\begin{array}{l} ~ r \to ~ (p \lor q) \\ \equiv\sim r \to (~ p \land ~ q) \end{array}$

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