Math Questions 17.2 - Operations with Sets

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The following math revision questions are provided in support of the math tutorial on Operations with Sets. In addition to this tutorial, we also provide revision notes, a video tutorial, revision questions on this page (which allow you to check your understanding of the topic) and calculators which provide full, step by step calculations for each of the formula in the Operations with Sets tutorials. The Operations with Sets calculators are particularly useful for ensuring your step-by-step calculations are correct as well as ensuring your final result is accurate.

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Operations with Sets Revision Questions

1. . Two sets A = {3, 5, 8, 11, 14} and B = {4, 5, 11, 13} are given. Which of the following is TRUE?

1. A ∪ B = {3, 4, 5, 5, 8, 11, 11, 13, 14}
2. A ∩ B = {3, 5, 11}
3. A - B = {3, 4, 8, 14}
4. B \ A = {4, 13}

Reveal AnswerCorrect Answer: D

2. . Which of the following sets is indicated by the yellow-coloured region in the figure below?

1. U - (A ∩ B)
2. (A \ B ∪ B \ A)'
3. (A ∩ B)'
4. U \ (A ∪ B)

Reveal AnswerCorrect Answer: B

3. . Which of the following sets is the complement of the yellow-coloured region in the figure below?

1. A ∪ B
2. A ∩ B
3. U - A ∩ B
4. U - A ∪ B

Reveal AnswerCorrect Answer: D

4. . Two sets A = {1, 2, 3, a, b, c} and B = {3, 4, c, d} and the universal set U = {1, 2, 3, 4, 5, a, b, c, d, e} are given. What is the set X = {3, c} in terms of the above sets?

1. X = U - (A' ∪ B')
2. X = U - (A \ B)
3. X = (A ∪ B)'
4. X = U - (A \ B ∪ B \ A)

Reveal AnswerCorrect Answer: A

Hint!

5. . Two sets A and B with some common elements and the universal set U containing them are given. Which of the following is TRUE about them?

1. A \ B = (U - B) \ (A ∩ B)
2. A ∪ B = U - A ∩ B
3. (A ∪ B) ∩ (U - A) = ∅
4. U' - A ∩ B = A ∪ B

Reveal AnswerCorrect Answer: A

6. . The sets A = {3, 5, 7, 10, 12} and B = {7, 8, 10, 11, 12, 13} are given. What is A ∪ B - (B \ A) - (A \ B)?

1. {7, 10}
2. {7, 10, 12}
3. {3, 5, 7, 10, 11, 12, 13}
4. {10, 11, 12, 13}

Reveal AnswerCorrect Answer: B

7. . Two sets A = {3, 5, c, d, e} and B = {2, 5, 7, c, d, f} are given. In addition, U - (A ∪ B) = {1, a} is given, where U is the universal set. Which set represents the complement of A (i.e. A')?

1. A' = {1, 2, 5, 7, a, c, d, f}
2. A' = {1, 3, 5, a, c, d, e}
3. A' = {1, 2, 7, a, f}
4. A' = 1, 2, 7, a, c, d}

Reveal AnswerCorrect Answer: C

8. . Two non-zero intersecting sets A and B are given. They take the values from the same universal set U. Which of the following is TRUE about these sets?

1. A ∩ B′ = A - B
2. A ∪ B' = B - A
3. A \ B = U - (A ∪ B) - (A ∩ B)
4. A' ∩ B' = A ∪ B

Reveal AnswerCorrect Answer: A

9. . Which set is represented by the shaded region in the number line below?

1. {x ∈ N, -1 < x < 4}
2. {x ∈ R, -1 ≤ x < 4}
3. {x ∈ R, -1 < x < 4}
4. {x ∈ N, -1 ≤ x ≤ 4}

Reveal AnswerCorrect Answer: C

10. . Set A contains 12 elements, set B contains 15 elements where 4 are common elements of these two sets and the universal set U - where both sets take the values - contains 30 elements in total. What is the number of elements of (A ∪ B)'?

1. 3
2. 7
3. 8
4. 11

Reveal AnswerCorrect Answer: B

11. . In a group of 29 students, 16 students like math, 12 students like physics and 5 students like both these subjects. How many students don't like any of these subjects?

1. 0
2. 1
3. 6
4. 23

Reveal AnswerCorrect Answer: C

12. . In a group of people, there are 17 men and 21 women. 22 people from this group are married, where 5 couples are part of the group, while the rest are single. What is the number of people in the group who don't have their consort in the group or who are single?

1. 38
2. 28
3. 15
4. 10

Reveal AnswerCorrect Answer: B

Whats next?

Enjoy the "Operations with Sets" practice questions? People who liked the "Operations with Sets" practice questions found the following resources useful:

1. Practice Questions Feedback. Helps other - Leave a rating for this practice questions (see below)
2. Sets Math tutorial: Operations with Sets. Read the Operations with Sets math tutorial and build your math knowledge of Sets
3. Sets Revision Notes: Operations with Sets. Print the notes so you can revise the key points covered in the math tutorial for Operations with Sets
4. Check your calculations for Sets questions with our excellent Sets calculators which contain full equations and calculations clearly displayed line by line. See the Sets Calculators by iCalculator™ below.
5. Continuing learning sets - read our next math tutorial: Sets Definition and Notation. Representing Sets

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