Question

If \(p\rightarrow (q∨\sim r)\) is false, then the truth values of \((p\leftrightarrow q)∧r\) and \(\sim p\rightarrow \sim q\) are :

• A. \(T,T\)
• B. \(T,F\)
• C. \(F,T\)
• D. \(F,F\)

Hint:

A conditional is false only when the antecedent is true and the consequent false.

Answer 1

The Correct Option is C

Step 1: Solve for p, q, r
The only assignment that makes the given statement false is $p=T,q=F,r=T$.

Step 2: Evaluate
$(T\leftrightarrow F)=F$, so the first statement is F. For the second, $\sim p=F$, and a false antecedent gives T. Option (C).

Final Answer:
Truth values $(F,T)$, option (C). \[ \boxed{F,\ T} \]