Q. 105.0( 2 Votes )

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

Answer :

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


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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