5. Let s : NN, where for each ne N, s(n) is the sum of the distinct natural number divisors of n. This is the sum of the divisors function that was introduced in Preview Activity 2 from Section 6.1. Is s an injection? Is s a surjection? Justify your conclusions. 6. Let d: NN, where d(n) is the number of natural number divisors of n. This is the number of divisors function introduced in Exercise (6) from Section 6.1. Is the function d an injection? Is the function d a surjection? Justify your conclusions. * 7. In Preview Activity 2 from Section 6.1, we introduced the birthday func- tion. Is the birthday function an injection? Is it a surjection? Justify your conclusions. 8. (a) Let f :ZxZZ be defined by f(m, n) = 2m+n. Is the function f an injection? Is the function f a surjection? Justify your conclusions. (b) Let g:ZxZZ be defined by g (m.n) = 6m+3n. Is the function g an injection? Is the function g a surjection? Justify your conclusions. 9. (a) Let f:RxR RxR be defined by f(x, y) = (2x. x + y). Is the function f an injection? Is the function fa surjection? Justify your conclusions. (b) Let g: ZxZ ZxZ be defined by g(x, y) = (2x, x + y). Is the function g an injection? Is the function g a surjection? Justify your conclusions.