Q. 2 C5.0( 2 Votes )

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

f3 = {(a, x), (b, x), (c, z), (d, z)}; A = {a, b, c, d}, B = {x, y, z}

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,


f3 = {(a, x), (b, x), (c, z), (d, z)}


A = {a, b, c, d}, B = {x, y, z}


Thus we can clearly see that


Check for Injectivity:


Every element of A does not have different image from B


Since,


f3(a) = x = f3(b) and f3(c) = z = f3(d)


Therefore f is not One – One function


Check for Surjectivity:


Also each element of B is not image of any element of A


Hence f is not Onto.


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