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JEE Main 201816 AprilOnline

Exam: JEE Main
Year: 2018
Date: 16 April
Mode: Online
Subject: Mathematics
Chapter: Mathematical Reasoning

JEE Main 2018 · 16 April · Online · Mathematics · Mathematical Reasoning

If p → (~ p ∨ ~ q) is false, then the truth values of p and q are,...

If

p \to

\left(~ p ∨ ~ q\right)

is false, then the truth values of

p and

q

are, respectively

Options

A $F, F$
B $T, T$
C $F, T$
D $T, F$

Correct answer

B. $T, T$

Step-by-step solution

$p \to q$ has truth value false only when $p$ is true & $q$ is false. Hence, truth value of $p$ is true.

Now, $~ p ∨ ~ q$ is false only when $~ p$ & $~ q$ both are false.
Hence, $p$ and $q$ are both true.

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