(C) The logical statement $r: p \to (\sim p \vee q)$ has a truth value $F$.An implication $A \to B$ is false if and only if $A$ is true and $B$ is fal

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(C) The logical statement $r: p \to (\sim p \vee q)$ has a truth value $F$.An implication $A \to B$ is false if and only if $A$ is true and $B$ is false.Therefore,$p$ must be $T$ and $(\sim p \vee q)$ must be $F$.For the disjunction $(\sim p \vee q)$ to be $F$,both $\sim p$ and $q$ must be $F$.Since $\sim p$ is $F$,it implies $p$ is $T$.Thus,$p$ is $T$ and $q$ is $F$.

Class 11 Mathematics Mathematical Reasoning Mathematical logic

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Let $p$ and $q$ be any two logical statements and $r: p \to (\sim p \vee q)$. If $r$ has a truth value $F$,then the truth values of $p$ and $q$ are respectively

JEE MAIN 2013 All JEE MAIN

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

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Mathematical Reasoning

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Which of the following are pairs of equivalent circuits?

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Let $p$ and $q$ be any two logical statements and $r: p \to (\sim p \vee q)$. If $r$ has a truth value $F$,then the truth values of $p$ and $q$ are respectively

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Which of the following sentences are statements? Give reasons for your answer.The square of a number is an even number.

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Which of the following sentences are statements? Give reasons for your answer.
The square of a number is an even number.

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If $x, y \in \mathbb{Z}$ are such that $x$ and $y$ are odd,then $xy$ is odd.

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$p:$ The sum of an irrational number and a rational number is irrational (by contradiction method).