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
⇒ 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
Given relation is a function
Since more than one person may have the same mother
Function, not One – One (injective) but Onto (Surjective)
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