an explicit formula for a function from the set of integers to the set of positive integers that isa) one-to-one, but not onto.________________b) onto, but not one-to-one.________________c) one-to-one and onto.________________d) neither one-to-one nor onto.

Solution:Step 1 :We have to formulate explicit formula for a function from the set of integers to the set of positive integers.Step 2:(a) Ans ; explicit formula for this function is if and It is one to one because non negative number map to even number, starting with 2,negative number map to odd number starting with 3.It is not onto since 1 is not the image of any integer. Step 3 :(b) Ans : explicit formula for this function isIt is onto because i is the image of ,it is not one-to-one because