If p ⇒ (q vee r) is false, then truth values of p, q, r are respectively

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Mathematical Reasoning

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If $p \Rightarrow (q \vee r)$ is false, then the truth values of $p, q, r$ are respectively

A

$T, F, F$

B

$F, F, F$

C

$F, T, T$

D

$T, T, F$

Solution

(a) $p \Rightarrow q$ is false only when $p$ is true and $q$ is false.

$p \Rightarrow q$ is false when $p$ is true and $q \vee r$ is false, and $q \vee r$ is false when both $q$ and $r$ are false.

Hence truth values of $p, q$ and $r$ are respectively $T, F, F.$

Standard 11

Mathematics

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