Question

Define a function as a set of ordered pairs.

Answer 1

Function = Let A and B be two non-empty sets. A relation f from A to B, i.e., a sub-set of $A\times B$, is called a function (or a mapping or a map) from A to B, if
i) For each $aϵA$ there exists $bϵB$ such that $(a,b)ϵf$
If $(a,b)ϵf$, then 'b' is called the image of 'a' under f.
If a function f is expressed 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.