Every non-zero subset of `A xx B` defined a relation from set `A` to set `B.`

Relation is a linear operation which establishes relationship between the element's of two set's according
to some definite rule of relationship.

`R: {(a, b) | (a, b) in A xx B` and `a quadRquadb}`

`text(Eg: 1 )quadquad``A` is `{2, 3,5}` and `quadquadB` is `{1, 4, 9, 25, 30}`

`quadquadquadquad` If `aRb -> b` is square of `a`

Discreet element of relation are `{(2, 4), (3, 9), (5, 25)}`

`text(Eg: 2 )quadquadA = {`Jaipur, Patna, Kanpur, Lucknow`}`

`quadquadquadquadB = {`Rajasthan, Uttar Pradesh, Bihar`}`

`quadquadquadquadquad aRb -> a` is capital of `b,`

`A xx B =` {(Jaipur, Rajasthan), (Patna, Bihar), (Lucknow, Uttar Pradesh)}


`text(Important points : )`

1. Any subset of `A xx A` is said to be a relation on A.
2. If A has m elements and B has n elements, then `A xx B` has `m xx n` elements and total number of different relations from A to B is `2^(mn).`
3. If `R = A xx B,` then Domain `R = A` and Range `R = B.`

4. The domain as well as range of the empty set `phi` is `phi .`

If `A= D o m R` and `B = Ran \ \ R,` then we write `B= R [A] .`