Section 1.5

• 14. Prove by first proving that the left-hand side is a subset of the right, then prove that the right-hand side is a subset of the left.
• 20. a) We cannot conclude that A = B. Consider the case when A and B are both subsets of C. b) We cannot conclude that A = B. Consider C being the empty set.
• 22. {2, 5}
• 24. Fill in all of A and B, but not A INTERSECT B.
• 26. Can do by truth tables.
• 34. Show by labelling all seven partitions in the Venn diagram and consider the cardinality of each and how many times the elements of each partition get counted.
• 44. Take the bitwise OR (for union) or AND (for intersection) of all the bit strings for the sets.
• 46. n + 1
• 48. a) share equipment, A UNION B. b) departments use minimum, A INTERSECT B. c) B - A. d) no sharing. A + B.
• 50. {0.6 Alice, 0.9 Brian, 0.4 Fred, 0.9 Oscar, 0.7 Rita}