Universal Set Quiz - CBSE Class 11 Mathematics

Free practice quiz: Universal Set (CBSE Class 11 Mathematics). 20 multiple-choice questions with answers and explanations. Play online, no sign-up needed.

This CBSE Class 11 Mathematics practice quiz has 20 multiple-choice questions on Universal Set, and 20 of them come with an explanation. Try the 5 sample questions below (tap an option to check yourself), then play the full quiz online. No sign-up needed.

Sample questions

1. In the context of sets, what is a universal set?

   1. A set containing all possible sets
   2. A set that contains all elements under discussion
   3. A set with no elements
   4. A set with exactly one element
   Show answer

   Answer: B. A set that contains all elements under discussion

   A universal set, typically denoted by U, is a set that contains all the objects under consideration for a particular discussion or problem.

2. Identify the universal set from the following: A = {1, 2}, B = {2, 3, 4}, C = {1, 2, 3, 4}.

   1. A
   2. B
   3. C
   4. None of them
   Show answer

   Answer: C. C

   The universal set should contain all elements from the sets in discussion. Here, C = {1, 2, 3, 4} has all elements from A and B, making it the universal set.

3. Consider the universal set U as all even numbers. If A = {2, 4, 6, 8}, what is the intersection of A with U?

   1. A
   2. U
   3. {}
   4. {2, 4, 6, 8, ...}
   Show answer

   Answer: A. A

   The intersection of any set with the universal set includes only those elements which are in both sets. Hence, A ∩ U = A = {2, 4, 6, 8}.

4. Given the set conditions A = {x | x is a multiple of 3} and U = {x | x < 30, x ∈ N}, what is A̅?

   1. {x | x is not a multiple of 3, x < 30}
   2. {x | x > 30}
   3. {x | x > 10}
   4. {x | x < 10}
   Show answer

   Answer: A. {x | x is not a multiple of 3, x < 30}

   Within the universal set U, the complement A̅ includes numbers that are not multiples of 3, ensuring x is still less than 30.

5. Which element surely does not belong to the universal set if U = {x | x < 100, x ∈ N}?

   1. 100
   2. 99
   3. 50
   4. 1
   Show answer

   Answer: A. 100

   The universal set consists of natural numbers less than 100, so 100 does not belong to U.

More questions in this quiz

Answers and explanations are in the full quiz.

1. If U is the universal set and A is a set such that A ⊆ U, which statement is TRUE?
2. If the universal set is U = {1, 2, 3, 4, 5} and A = {2, 3}, what is the complement of A?
3. Given U = {a, b, c, d, e} and B = {c, d}, find B'.
4. What is the intersection of the universal set U with any set A?
5. The universal set U contains all odd numbers from 1 to 19. What is the complement of the set D = {3, 7, 11}?
6. If A = {x | x is a positive integer less than 10} and U = {x | x is a positive integer less than 20}, what is the complement of A with respect to U?
7. In a scenario where U is the set of all whole numbers, what would be the complement of the set W = {0, 2, 4, 6, 8}?
8. If U = {1, 2, 3, ..., 10} and F is a finite set such that F ⊆ U, which of these cannot be the complement of F?
9. If A = {x ∈ Z | x^2 < 16} and U = Z, the set of all integers, what is A̅?
10. If U is the universal set of real numbers, and A = {x | x is an irrational number}, what is A̅?
11. For the universal set U = {x | x is a letter in the English alphabet}, determine the complement of B = {vowels}?
12. The universal set U = {x | x > 0}. Let C = {x | x is a prime number}. What is C̅?
13. In set theory, if U is the universal set and D = ∅, what is D̅?
14. The universal set U consists of all real numbers. If E = {x | x is negative}, what is the set E̅?
15. Suppose U = {x ∈ R | -5 ≤ x ≤ 5}. Which of the following statements must be true for the complement of F = {x | x < 0}?

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