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Which of the following statements is logically equivalent to p ⇔ q?

1. (p ∧ q) ∨ (p ∧ q)
2. (p ⇒ q) ∧ (q ⇒ p)
3. (p ∧ q) ∨ (q ⇒ p)
4. (p ∧ q) ⇔ (q ∨ p)

Correct answer: (p ⇒ q) ∧ (q ⇒ p)

Solution

The statement p ⇔ q means that p is true if and only if q is true, which is precisely captured by the conjunction of the implications (p ⇒ q) and (q ⇒ p). This indicates that both conditions must hold for the biconditional to be true.

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