Sets

Topics in this chapter

• Set Representations and Membership
• Set Operations
• Set Identities and De Morgan’s Law
• Subsets and Power Sets
• Set Cardinality and Inclusion-Exclusion
• Cartesian Products and Ordered Pairs
• Intervals of Real Numbers

Cheat sheet

Practice questions

1. Question 1Q-453578

   If A = {1, 2, 3}, how many subsets does A have?

   1. A.3
   2. B.6
   3. C.8
   4. D.9
   See the answer and solution
2. Question 2Q-B2CCE0

   Let A = {1, 2, 3, 4} and B = {3, 4, 5}. Which statement is necessarily true?

   1. A.A is a subset of B
   2. B.B is a subset of A
   3. C.A ∩ B = {3, 4}
   4. D.A ∪ B = {1, 2, 3, 4}
   See the answer and solution
3. Question 3Q-37FF58

   In the universal set U = {1, 2, 3, ..., 12}, let A be the set of multiples of 2 and B be the set of multiples of 3. How many elements belong to neither A nor B?

   1. A.2
   2. B.4
   3. C.5
   4. D.6
   See the answer and solution
4. Question 4Q-8250B6

   For subsets A and B of a universal set U, prove that (A ∪ B)′ = A′ ∩ B′.

   See the answer and solution
5. Question 5Q-82E434

   Which of the following is the correct set-builder form of the set {2, 4, 6, 8, 10}?

   1. A.{x : x is an odd natural number less than 11}
   2. B.{x : x is an even natural number less than 11}
   3. C.{x : x is a prime natural number less than 11}
   4. D.{x : x is a natural number less than 10}
   See the answer and solution