Q62 / 150 · MHT CET 2026 (20 April Shift 2) · Mathematics
If $\sim p \vee q$ is false then which of the following is correct?
- A$p \leftrightarrow q$ is $T$
- B$p \rightarrow q$ is $T$
- Correct answerC$q \rightarrow p$ is $T$
- D$q \rightarrow p$ is $F$
Solution
Given $\sim p \vee q$ is false.
A disjunction is false only when both of its components are false.
Therefore, $\sim p$ is false and $q$ is false.
This implies $p$ is true ($T$) and $q$ is false ($F$).
Checking the given options:
$p \leftrightarrow q \equiv T \leftrightarrow F \equiv F$
$p \rightarrow q \equiv T \rightarrow F \equiv F$
$q \rightarrow p \equiv F \rightarrow T \equiv T$
Thus, $q \rightarrow p$ is $T$.
Answer: $q \rightarrow p$ is $T$
A disjunction is false only when both of its components are false.
Therefore, $\sim p$ is false and $q$ is false.
This implies $p$ is true ($T$) and $q$ is false ($F$).
Checking the given options:
$p \leftrightarrow q \equiv T \leftrightarrow F \equiv F$
$p \rightarrow q \equiv T \rightarrow F \equiv F$
$q \rightarrow p \equiv F \rightarrow T \equiv T$
Thus, $q \rightarrow p$ is $T$.
Answer: $q \rightarrow p$ is $T$
Hence, the correct answer is option: 'C'.