Within propositional logic, the term equivalence is used in either of the following two ways: (1) as a particular type of propositional statement or (2) as the logical operator used to form an "equivalence" statement. In order to develop a precise...

In mathematics, a generalization of the idea of equality between elements of a set. All equivalence relations (e.g., that symbolized by the equals sign) obey three conditions: reflexivity (every element is in the relation to itself), symmetry (element...

. Any SYMMETRIC AND TRANSITIVE relation, e.g. equal in size to. Its terms are equivalent in the sense that there is some determinable property, like size, which they all have to the same degree or in the same determinate form, and whatever any of them...

in logic and mathematics, the formation of a proposition from two others which are linked by the phrase “if, and only if.” The equivalence formed from two propositions p and q also may be defined by the statement “p is a necessary and...

In mathematics, an equivalence relation is a binary relation between two elements of a set which groups them together as being "equivalent" in some way. Let a, b, and c be arbitrary elements of some set X. Then "a ~ b" or "a ≡ b" denotes that a is...