First slide

Introduction to mathematical reasoning

Question

lf $p \to (q \lor r)$ is false, then the truth values of p, q and r are, respectively,

Moderate

A

T, T, F
B

F, F, F
C

F, T, T
D

T, F, F

Solution

$p \to q$ is false only when p is true and q is false.
Therefore, $p \to (q \lor r)$ is false when p is true and $q \lor r$ is false.
$q \lor r$ is false only when both q and r are false.
Hence, truth values of p, q and r are, respectively, T, F and F.

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