PART C 8 marks 1. (2 marks) Find a triple set S such that: (a) {} does not belong to S and {{}} does not belong to S. (b) {} does not belong to S and {{}} belongs to S. () {} belongs to S and {{}} does not belong to S. (d) {} belongs to S and {{}} belongs to S. 2. (0.5 mark) What is the cardinality of the set { &, {J}, J, {J, {J}} } ? Justify your answer. 3. (1.5 marks) Let A be a set and let B be the set of all the subsets of A. (a) What is B if A={0}? (b) What is B if A={-1, 1}? (c) What is B if A={-1,0, 1}? 4. (2 marks) Let A be a set and let B be the set of all the subsets of A. (a) Is it possible for B to contain exactly one set of cardinality 7? If the answer 1s positive, what can you say about A? Justify your answers. (b) Is it possible for B to contain exactly two sets of cardinality 7? If the answer is positive, what can you say about A? Justify your answers