a) Define what it means for a function from the set of positive integers to the set of positive integers to be one-to-one.

b) Define what it means for a function from the set of positive integers to the set of positive integers to be onto.

c) Give an example of a function from the set of positive integers to the set of positive integers that is both one-to-one and onto.

d) Give an example of a function from the set of positive integers to the set of positive integers that is one-to-one but not onto.

e) Give an example of a function from the set of positive integers to the set of positive integers that is not one-to-one but is onto.

f) Give an example of a function from the set of positive integers to the set of positive integers that is neither one-to-one nor onto.

SOLUTION

a)Step 1

Let f is a function from the set of positive integers to set of positive integers.

A function is said to be a one-one function,if every positive integer in the domain

is associated with one and only one positive integer in the co- domain.

b)