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On the set of integers Z, define f : Z t...

On the set of integers Z, define f : `Z to Z` as
`f(n)={{:((n)/(2)",",,"n is even."),(0",",,"n is odd."):}`
Then, f is

A

injective but not surjective

B

Neither injective nor surjective

C

surjective, but not injective

D

bijective

Text Solution

Verified by Experts

The correct Answer is:
C
Given, `f(n)={{:((n)/(2)",""n is even"),(0",""n is odd"):}`
Here, we see that for every odd values of n, it will give zero. It means that it is a many-one function.
For every even values of n, we will get a set of integers `(-oo,oo)`. So, it is onto. Hence, it is surjective, but not injective.
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