Q61 / 150 · MHT CET 2026 (18 April Shift 1) · Mathematics
The negation of the converse of $p \vee q$ is
- A$\sim p \vee q$
- Correct answerB$p \wedge q$
- C$p \vee \sim q$
- D$\sim p \wedge \sim q$
Solution
The statement $p \vee q$ can be expressed as a conditional statement: $\sim p \rightarrow q$.
The converse of a conditional statement $A \rightarrow B$ is $B \rightarrow A$.
Therefore, the converse of $\sim p \rightarrow q$ is $q \rightarrow \sim p$.
The statement $q \rightarrow \sim p$ is logically equivalent to $\sim q \vee \sim p$.
The negation of this converse is $\sim(q \rightarrow \sim p) \equiv \sim(\sim q \vee \sim p)$.
Using De Morgan's laws, $\sim(\sim q \vee \sim p) \equiv q \wedge p \equiv p \wedge q$.
Answer: $p \wedge q$
The converse of a conditional statement $A \rightarrow B$ is $B \rightarrow A$.
Therefore, the converse of $\sim p \rightarrow q$ is $q \rightarrow \sim p$.
The statement $q \rightarrow \sim p$ is logically equivalent to $\sim q \vee \sim p$.
The negation of this converse is $\sim(q \rightarrow \sim p) \equiv \sim(\sim q \vee \sim p)$.
Using De Morgan's laws, $\sim(\sim q \vee \sim p) \equiv q \wedge p \equiv p \wedge q$.
Answer: $p \wedge q$
Hence, the correct answer is option: 'B'.