The definition of relation in discrete mathematics refers to the connection and correspondence between objects.

That is, let A 1, A2, A3, ... An be n sets, and the subset f...an of the set A 1× A2× is called the n-ary relation on a 1, a2, A3, ... an. In particular, the subset R of the set A×B is called the binary relation on the sets A and B, which is called the relation for short.

For x∈A, y∈B, R is the binary relationship between A and B. If (X, y)∈R, it is said that X and Y have a relationship R, which is denoted as xRy；; If (x，y)？ R is called X, and Y has nothing to do with R. If B=A, R is called binary relation on A..

The characteristics of this relationship are:

Any subset of 1 and A×A is a relation on a.

2. If ∣A∣=n, then the relationship on A has 2 n? Power one.

3. There are three special relationships on A, namely: empty relationship? , the global relation Ea=A×A, and the equality relation Ia={(x, x)∣x∈A}.

4. the inverse set of r = ea-r = a× a-r.

For example, let A={ 1, 2,3,4}, a× a = {( 1, 1), (1, 2), (1, 3), (/kloc-

1、R 1={(2， 1)、(3， 1)、(4， 1)、(3，2)、(4，2)、(4，3)}

2、R2={( 1， 1)，(2，2)，(3，3)，(4，4)}

3、R3={( 1， 1)，( 1，2)，( 1，3)，( 1，4)，(2，2)，(2，4)，(3，3)，(4，4)}

4、R4={( 1， 1)，(2，2)，( 1，2)，(2， 1)}

All of the above are related to A.