please do all the questions!

(a) (10 points) Prove the following result about sets. Do not use Venn Diagrams, Membership Tables, or set identities. (AB)C=A(BC) (b) (5 points) For each of the following sets, determine whether they are countable or uncountable: i. R+ ii. P(N) iii. RQ iv. The set of all prime numbers v. {1,3,5,7}