Question

Consider the following logical statements:
R: If \(p \rightarrow q\) is false, then \(p \vee q\) is false.
S: If \(p \leftrightarrow q\) is false, then \(p \vee q\) is false.
Evaluate the truth values of R and S.

• A. Both R and S are true
• B. R is true and S is false
• C. R is false and S is true
• D. Both R and S are false

Hint:

An implication \( P \rightarrow Q \) is only false when the premise \( P \) is True and the conclusion \( Q \) is False.
If you can find one case where the premise is met but the conclusion is not, the statement is false.

Answer 1

The Correct Option is D