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 …