Define a function as a set of ordered pairs. - Vidyadip

Question

Define a function as a set of ordered pairs.

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Answer

Function: Let A and B be two non-empty sets. A relation A to B i.e., a sub-set of A × B, is called a function (or a mapping a map) from A to B, if

For each $\text{a}\in\text{A}$ there exists $\text{b}\in\text{B}$ such that $(\text{a},\text{b})\in\text{f}$
$(\text{a},\text{b})\in\text{f}$ and $(\text{a},\text{c})\in\text{f}$

$\Rightarrow\text{ b} =\text{c}$

If $(\text{a},\text{b})\in\text{f},$ then 'b' is called the image of 'a' under f.

If a function is expresed as the set of ordered pairs, the domain f is the set of all first components of members of f and the range of f is the set of second components of members of f.

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