Introduction to Relations

In this class, We discuss Introduction to Relations.

The reader should have prior knowledge of set theory basics. Click Here

Relation:

A set of ordered pairs defines a binary relation or simple relation.

Example:

A = {(1,2), (5,6), (8,9)}

The relation can be defined

1) On two sets

2) On a single set

Example:

Take two sets

A = {5, 6, 9}

B = {7, 10, 11}

Relation “<“

R = {(5,7), (5,10), (5,11), (6,7), (6,10), (6,11), (9,10), (9,11)}

Example 2:

Take a set of N

N means a set of natural numbers.

N = {0, 1,2,3 . . . }

Relation S = {(x, x^2)/x ∈ N}

S = {(0,0), (1,1), (2,4), (3,9), . . . }

Range and domain of a relation

Domain:

The domain is a set of all the first elements in the ordered pairs.

S = {(1,2), (3,4), (a, t), (p,q)}

Domain = D(S) = {1, 3, a, p}

Range:

The range is a set of all second elements in the ordered pairs.

R(S) = {2, 4, t, q}