Q. 2 B3.8( 6 Votes )

Which of the following functions from A to B are one – one and onto?

f2 = {(2, a), (3, b), (4, c)}; A = {2, 3, 4}, B = {a, b, c}

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


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, As given,


f2 = {(2, a), (3, b), (4, c)}


A = {2, 3, 4}, B = {a, b, c}


Thus we can see that


Check for Injectivity:


Every element of A has a different image from B


Hence f is a One – One function


Check for Surjectivity:


Also, each element of B is an image of some element of A


Hence f is Onto.


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