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.
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In the context of sets, what is a universal set?
- A set containing all possible sets
- A set that contains all elements under discussion
- A set with no elements
- A set with exactly one element
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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.
Identify the universal set from the following: A = {1, 2}, B = {2, 3, 4}, C = {1, 2, 3, 4}.
- A
- B
- C
- None of them
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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.
Consider the universal set U as all even numbers. If A = {2, 4, 6, 8}, what is the intersection of A with U?
- A
- U
- {}
- {2, 4, 6, 8, ...}
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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}.
Given the set conditions A = {x | x is a multiple of 3} and U = {x | x < 30, x ∈ N}, what is A̅?
- {x | x is not a multiple of 3, x < 30}
- {x | x > 30}
- {x | x > 10}
- {x | x < 10}
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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.
Which element surely does not belong to the universal set if U = {x | x < 100, x ∈ N}?
- 100
- 99
- 50
- 1
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Answer: A. 100
The universal set consists of natural numbers less than 100, so 100 does not belong to U.