Relations and Functions

- A relation
*R*from a set*A*to a set*B*is a subset of*A*×*B*obtained by describing a relationship between the first element*a*and the second element*b*of the ordered pairs in*A*×*B*. That is,*R*⊆ {(*a*,*b*) ∈*A*×*B*,*a*∈*A*,*b*∈*B*} - The domain of a relation
*R*from set*A*to set*B*is the set of all first elements of the ordered pairs in*R*. - The range of a relation
*R*from set*A*to set*B*is the set of all second elements of the ordered pairs in*R*. The whole set*B*is called the co-domain of*R*. Range ⊆ Co-domain - A relation
*R*in a set*A*is called an empty relation, if no element of*A*is related to any element of*A*. In this case,*R*= ⊂*A*×*A*

**Example:** Consider a relation *R* in set *A* = {3, 4, 5} given by *R* = {(*a*, *b*): *a ^{b}* < 25, where

*a*,

*b*∈

*A*}. It can be observed that …

To view the complete topic, please