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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