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

Now, f : A → A where A = {1, 2, 3} and its an Onto function

To Prove: – A is a One – One function

Let's assume f is not Onto function,

Then,

There must be two elements let it be 1 and 2 in Domain A = {1, 2, 3} whose images in co–domain A = {1, 2, 3} is same.

Also, Image of 3 under f can be only one element.

Therefore,

Range set can have at most two elements in co – domain A = {1, 2, 3}

⇒ f is not an onto function

Hence it contradicts

⇒ f must be One – One function

Hence Proved