Question

Negation of the statement \( (\rho \land r) \rightarrow (r \lor q) \) is

• A. \( (\rho \land r) \land (\neg r \land \neg q) \)
• B. \( \neg (\rho \land r) \rightarrow (r \lor q) \)
• C. \( \neg (\rho \lor r) \rightarrow \neg (r \land q) \)
• D. \( (\rho \land r) \lor (r \lor q) \)

Hint:

The negation of an implication is found by retaining the premise and negating the conclusion.

Answer 1

The Correct Option is A

The negation of a conditional statement \( p \rightarrow q \) is \( p \land \neg q \). So the negation of the given statement \( (\rho \land r) \rightarrow (r \lor q) \) is \( (\rho \land r) \land (\neg r \land \neg q) \).