Q. 26

Mark the correct alternative in each of the following:

A function f from the set of natural, numbers to the set of integers defined by



A. neither one-one nor onto

B. one-one but not onto

C. onto but not one-one

D. one-one and onto both

Answer :

Given that a function f from the set on natural numbers to integers where



For n is odd


Let f(n) = f(m)



n = m


For n is even


Let f(n) = f(m)



n = m


So, f is one-one.


Also, each element of y is associated with at least one element of x, so f is onto.


Hence, f is one-one and onto.

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