How do you define logical equivalence?

Logical equivalence is the relation that holds between two statements that follow from each other. In other words, two statements are logically equivalent if each is a logical consequence of the other.

P: Smith has exactly two cars.

Q: There is a number n such that n is an even prime and such that n is the number of Smith’s cars.

Q is a logical consequence of P and P is a logical consequence of Q. Therefore, P and Q are logically equivalent.