Question

Define function. Give an example of a function from the set Z of integers to the set Z+ {0} of nonnegative

integers​

Answer 1

Answer:

f:X→Y

For a function to be one one or injective, every element in the domain is the image of at most one element of it's co-domain.

In simple words, no value of y must be same for 2 or more different values of x.

For f(x)=∣x∣, we see that f(a)=f(−a), for a∈Z

Hence, the function is not one one

For a function f:X→Y, to be surjective,

every element y in the co-domain Y must be linked with at least one element x in the domain.

Every element in the co-domain of f(x)=∣x∣ is linked to at-least one element in domain.

Thus, f(x)=∣x∣ is onto but not one one.