3 For each of the following problems determine if the given

3. For each of the following problems, determine if the given relation is a function. If it is not a function, explain why not. If it is a function, state the range and whether or not the function is injective or surjective, but you do not have to provide justification for this part.

(a) Let A = {5, 6} and B = {5, 7, 8} and S = {n : n 3 is an odd integer}. Define a relation R from A × B to S as R = {((a, b), s) : s|(a + b)}.

(b) Let A = {3, 17, 29, 45} and B = {4, 6, 22}. Define a relation R from A to B as R = {(a, b) : a+b is prime}.

Solution

a) function, not injective, not surjective.

b).not a function, since 29 in A has no image in B.