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RELATION & FUNCTION - RELATION AS AN ASSOCIATION BETWEEN TWO SETS

**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}**