Relation as an association between two sets (Mathematical Concepts) –
Consider the sentence ‘x’ is the capital of ‘y’
A few ordered pairs satisfying the sentence are (Moscow, Russia), (New Delhi, India), (Kathmandu, Nepal), (London, England), (Thimpu, Bhutan). Similarly, the ordered pairs.
{(9, 2), (8, 7), (6, 3), (3, 0)} satisfy the sentences ‘x is greater than y’ while (7, 9), (8, 3), (6, 4), (9, 5) do not.
From the above we can conclude that we can always form a set of ordered pairs from the given relation
A relation is a set of ordered pairs obtained by virtue of an association between two sets. Any set of ordered pairs is, therefore, a relation. The set of first components of the ordered pairs is called the domain and the set of second components is called the range.
For example, in the relation {(6, 8), (3, 7), (1, 2), (0, 1)} the domain is {6, 3, 1, 0} and the range is {8, 7, 2, 1}
Notation for Relation –
We use the letter ‘R’ to designate a relation. For example,
(i) R = {(1, 5), (4, 8), (2, 13), (16, 20)}
(ii) R = {(p, q) : p ∈ B, q ∈ G, q is the sister of p}
(iii) R = {(x, y) : x, y ∈ w, y > x}