Logical Equivalence

In mathematics, two statements are logically equivalent if they produce the same truth value in every case. For example, $P\land Q$ and $Q\land P$ are logically equivalent, as are $P\lor Q$ and $Q\lor P$ , and $P\iff Q$ and $Q\iff P$ . "x is greater than 7" and "x is not less than or equal to 7" are logically equivalent because they are both true or both false simultaneously for every real number x. A conditional ( $P\implies Q$ ) and its contrapositive ( $\neg Q\implies \neg P$ ) are always logically equivalent. For example, "if x is even, then x is divisible by 2" is logically equivalent to its contrapositive, "if x is not divisible by 2, then x is not even".