1.

Let A = {1, 2, 3}. Write all one – one from A to itself.

Answer»

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

So, f: A → B is One – One function

⇔ a≠b

⇒ f(a)≠f(b) for all a, b ∈ A

⇔ f(a) = f(b)

⇒ a = b for all a, b ∈ A

We have A = {1, 2, 3}

So all one – one functions from A = {1, 2, 3} to itself are obtained by re – arranging elements of A.

Thus all possible one – one functions are:

f(1) = 1, f(2) = 2, f(3) = 3

f(1) = 2, f(2) = 3, f(3) = 1

f(1) = 3, f(2) = 1, f(3) = 2

f(1) = 1, f(2) = 3, f(3) = 2

f(1) = 3, f(2) = 2, f(3) = 1

f(1) = 2, f(2) = 1, f(3) = 3


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