Truth value of a compound formula (b)

Short answer

((P∧¬Q)↔(Q∧R)) is true (F↔F), and (S∨¬Q) is true, so the implication is true. Truth value: TRUE.

If P = F, Q = T, S = T, R = F, then find truth value of: ((P ∧ ¬Q) ↔ (Q ∧ R)) → (S ∨ ¬Q)

Given P = F, Q = T, S = T, R = F. Formula: ((P ∧ ¬Q) ↔ (Q ∧ R)) → (S ∨ ¬Q)

Step	Sub-formula	Working	Value
1	¬Q	¬T	F
2	P ∧ ¬Q	F ∧ F	F
3	Q ∧ R	T ∧ F	F
4	(P ∧ ¬Q) ↔ (Q ∧ R)	F ↔ F	T
5	S ∨ ¬Q	T ∨ F	T
6	whole: step 4 → step 5	T → T	T

Answer: the truth value is TRUE.

✓ Answer checked by Claude Opus 5.5 (high effort)

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