Only need help with part d I already know no such function e

Only need help with part d). I already know no such function exists.

For each part of this exercise, exhibit sets A, B, and C, with C strict subset A, and a function f: A rightarrow B satisfying the given conditions. Or, if no such function exists, show that none exists. (There is no need to get fancy here. In each case where such an f exists, an example can be constructed in which each of the sets A, B, C has at most two elements.) f is surjective and the restriction f|c is surjective. f is surjective but f|c is not surjective. f is injective and f|c is injective. f is injective but f|c is not injective.

Solution

Consider three sets A, B and C

C is contained in A

Since f from A to B is injective, f(a) = f(b) implies a=b for all a and b in A

Since C is contained in A, if we consider any two elements c and d from C they have to be in A also as C is

a subset of A

Hence f(c) = f(d) necessarily implies c = d as c and d are elements of A also

Hence no such function exists for which f: A to B is injective but f/C is not injective when C is a subset of A