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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