2. (12 points) For each of the following, determine whether it is true or false and then prove it (if it true) or disprove it (if it is false). In grading this question, we will check whether you correctly determined the truth value for each statement, but we may not grade all four proofs. (a) For sets A, B, if ACR and BCR and both are closed under addition then AnB is also closed under addition. (b) For sets A, B, if A R and R and both are closed under addition then AUB is also closed under addition. (c) For A a set, (d) For sets A, B, C if A n C = B n C then A = B