TIP: – One – One Function: – A function is said to be a one – one functions or an injection if different elements of A have different images in B.

So, is One – One function

⇔ a≠b

⇒ f(a)≠f(b) for all

⇔ f(a) = f(b)

⇒ a = b for all

Onto Function: – A function is said to be a onto function or surjection if every element of A i.e, if f(A) = B or range of f is the co – domain of f.

So, is Surjection iff for each , there exists such that f(a) = b

Here, It is given (x, y): x is a person, y is the mother of x

As we know each person “x” has only one biological mother

Thus,

Given relation is a function

Since more than one person may have the same mother

Function, not One – One (injective) but Onto (Surjective)