Discussion
Which one of the following is not equivalent to p ↔ q ?
Answer: C
The expression not equivalent to p ↔ q is (¬ p ∧ q) ∨ (p ∧ ¬ q).
That expression is true exactly when p and q differ, which is exclusive OR, the negation of p ↔ q.
The others are equivalent. (¬p ∨ q) is p → q and (p ∨ ¬q) is q → p, so their conjunction is p ↔ q, and option B writes the same thing with q → p. (¬p ∧ ¬q) ∨ (p ∧ q) is true exactly when p and q are equal, which is again p ↔ q.
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