Mark these as True or False. If False, then explain or give a counterexample. If True,...

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Mark these as True or False. If False, then explain or give a counterexample. If True, then prove/explain why. a. [x+y] = [x] + [y], where x is real (these are floor and ceiling functions). b. VxVyz ((z> x) A (z <y)), where the domain of x, y and z is all reals. c. If A and B are disjoint nonempty sets, then |A|≤ |A|+|B|. d. Let A, B, C be sets in some universe U. Then, A- (B-C)=(A-B) - C. e. {{0}} {{0}, {0}}. Mark these as True or False. If False, then explain or give a counterexample. If True, then prove/explain why. a. [x+y] = [x] + [y], where x is real (these are floor and ceiling functions). b. VxVyz ((z> x) A (z <y)), where the domain of x, y and z is all reals. c. If A and B are disjoint nonempty sets, then |A|≤ |A|+|B|. d. Let A, B, C be sets in some universe U. Then, A- (B-C)=(A-B) - C. e. {{0}} {{0}, {0}}.