CSE 253 (Discrete Structure) Homework#3 Due Date: 17 March, 2021 Q#1: Determine whether these statements are true or false. a) E{} b) {{}} {{ }, {}} Marks: 10 c) } E {} d) {} {{@}} e) {} c{{@}} f) {{@}} {{0}} Q#2: What is the cardinality of each of these sets? a) b){} c) {{}} d) {{}, {,{@}}} Q#3: Determine whether each of these functions is a bijection. If it is a bijection, prove it; if not a bijection, give a counterexample. i. f: RR: f(x) = x2 f: {1,2,3} (2): {(1,2). (2,2), (3,2)} f: {1,2,3} {1,2, 3): {(1,2), (1,3), (2,1), (2,2)} Q#4: Prove the square of an even number is an even number. Q#5: Can you conclude that A = B if A and B are two sets with the same power set? Why or why not? Q#6: Suppose that Ax B = , where A and B are sets. What can you conclude? Q#7: Suppose that A, B, and C are sets such that A S B and B SC. Show that A SC