Relations and Functions

If set A contains m elements and set B contains n elements, then the set A x B will have

Any subset of ordered pairs in A x B is called a relation from

A x B

Let A = {1, 2, 3} and B = {2, 4}, then A x B =

Function from A to B

A collection of ordered pairs (from the set A x B) constitute a special relation from A to B, which is called a function from A to B if we select the ordered pairs in such a way that:

Relations from A to B

Let A = {1, 2, 3, 4} and B = {2, 4, 5}

The following are all possible relations from A to B

R₁ = {(1, 2), (1, 5), (2, 2), (3, 4), (3, 5), (4, 5)}
R₂ = {(1, 4), (4, 2), (4, 5)}
R₃ = {(3, 2), (3, 4), (3, 5), (1, 4)}
R₄ = {(1, 4), (2, 5), (3, 2), (4, 4)}
R₅ = {(1, 2), (2, 5), (3, 4), (4, 4)}

Product with empty set

Let A = {1, 2, 3}, B = ∅, Then A x B = 

Domain of a Relation

In any relation (in the form of a set of ordered pairs), the set consisting of the ________ element of each pair constitutes the domain of the relation.

Given a domain of R, tell if it is a function