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RELATION & FUNCTION - DEFINITION OF FUNCTION

__DEFINITION OF FUNCTION -__

__Definition –__ A function is a is a special type of relation in
which no two different ordered pairs have the same first component.

**Stated directly in terms of a set of ordered pairs, the definition is as
given below.**

__Definition –__ A function is a set
of ordered pairs, no two of which have the same first components.

**Stated directly in terms of a
set of ordered pairs, the definition is as given below –**

__Definition –__ A function is a
set of ordered pairs, no two of which have the same first components. The set
{(0, 1), (1, 1)} is a function but the set {(1, 0), (1, 1)} is not a function
as first component is repeated

**A function is usually denoted by
f, g, h, F, G, H**

**Math Alert – By convention, the
empty set is not considered a function. A function is usually denoted by
letters f, g, F, G.**

**Thus, here, f = {(a, 1), (b, 2),
(c, 3), (d, 3)}**

**Range (f) ⊆ co-domain (f)**