In everyday use **relations concept means** an abstract type of connection **between two person or object**s, for stance (teacher, poor), **(mother, son),** **(husband, wife)**, (brother, sister), (friend, friend),** (house, owner)** in mathematics also some operations determine relationship between two numbers for example.Relations concept example in math example.

**(1) Greater than : (5,4)** or greater than sign mean > in math

**(2) square: (25,5)**

**(3) square root: (2,4)**

**(4) equal : (2×2,4)**

A relation is a set of** ordered pair** whose element are ordered a pair of relation number of objects. The relationship between the component of an ordered pair may or may not be mentioned.

## RELATIONS CONCEPT POINT

### (a) BINARY RELATION:

Let any set A and B be two non-empty, then any set of the Cartesian products A×B is called a binary relation or simply a relation from A to B.

#### (b) DOMAIN:

The set of the 1st element of the ordered pair forming a relation is called its domain.

#### (c) RANGE:

The set of 2nd elements of the ordered pairs formed a relation is called its range.

#### (d) RELATION ON A

If A is a non-empty set, any subset of A×A is called a relation in A OR on A

##### EXAMPLE

Let a, b, c be three children and x, y be two men such that father of two children a, b is x and father of c is y.

Defined relation between.

##### SOLUTION:

**C= set of children = {a, b, c} and F= set of fathers= {x, y}**

**C×F = {(.a, x), (.a, y), (b, x), (b, y), (c, x), (c, y)}**

**r = set of ordered pairs (children, father)**

**= C×F = {(.a, x), (b, x), (c, y)}**

**DOM r = {a, b, c}, Ran r = {x, y}**

**EXAMPLE: 2**

Let A = {1,2,3} Determine the **relation r such that x relation y,**

Iff x< y

**SOLUTION:↔**

A×A={(1,1), (1,2), (1,3), (2,1), (2,2), (2,3), (3,1), (3,2), (3,3)}

clearly required relation is such that

**r= {(1,2), (1,3), (2,3)}**, Domain. **r.={1,2} Ran r= (2,3)**

**RELATED POST:**