 Logical equivalence is used to construct compound propositions which are true if all simple propositions have the same truth value. It is symbolized by the triple bar symbol, which is also used in maths to represent numerical equality, or by the double arrow. Here are two propositions. P, Earth is a planet. Q, Earth is a solar satellite. Both propositions are true. Using the other logical connectives, we can construct the following true statements. As a conjunction, P and Q is true. As an inclusive disjunction, P or Q is true. And using the negative operator, we can define not P and not Q is false. And not P or Q is also false. All those statements that have the same truth value can now be defined as logically equivalent. The statement P and Q is equivalent to P or Q is true. And the statement not P and not Q is equivalent to not P or Q is also true. So equivalence produces a value of true if and only if both propositions are true or if and only if both propositions are false. Equivalent statements are important for the analysis of sentence meaning because they can freely replace one another without affecting the truth value.