3. (12+4 points) (a) For each of the following pairs of S and T determine whether |S| = |T| by providing a bijection from S to T if one exists (and prove it is a bijection). Otherwise, determine if |S| |T| by providing an injection from S to T if one exists. If neither exists, provide a justification. i. S = {n | k N such that n = 2k}, T = N ii. S = {n | n Z,|n|50}, T = {n | n is a prime number} iii. S = N, T=R-Q (b) So far, we have not defined the relation for infinite cardinality sets, only and =. Give a definition for |S| |T| where S, and T are infinite sets. Then, using the definition of , prove that your definition satisfies the following property: |S| |T| |T| |S|. Your definition should be along the lines of the definitions you've seen, and you are not allowed to define |S| |T| to be the same as |T| < |S|. 2