There are two propositions, P and Q. If the conclusion that Q can be established on the condition of P, it is said that P is a sufficient condition of Q; If p can be established by q, then p is a necessary condition for q; If P and Q can be mutually deduced (that is, whether P is derived from Q or Q is true), then P is a necessary and sufficient condition of Q, which is also called the equivalence of P and Q..

definition

If the relation R is reflexive, symmetric and transitive in the set A, it is called an equivalent relation on A. Is the relation R a Cartesian product? A subset of a× a.

The two elements X and Y in A have a relation R. If (X, y) ∈ R, we often abbreviate it as xRy. Reflexive: If any X belongs to A, then X is related to itself, that is, xRx；; Symmetry: Any X and Y belong to A. If X and Y have a relationship R, that is, xRy, then Y and X also have a relationship R, that is, yRx.

Transitivity: Any X, Y and Z belong to A. If xRy and yRz are equivalent, then xRz, X and Y have an equivalent relationship, which is called X, y R equivalence, sometimes called equivalence.