alleryStart learning →A, B ⊆ U satisfy A ∩ B = ∅ and A ∪ B = U. Which equality must hold?
- B = ∅
- B = A′
- B = A
- B = U
Show answer and solution
Correct answer: B. B = A′
B contains none of A and contains every element of U outside A, so B is the complement of A.
ICSE Class 8 Sets — practice questions — page 2
Explore 38 free Sets questions in ICSE Class 8 Mathematics. Open each question or exercise to read its content, reference answers and available explanation.
Practise Sets with Quill →Sets questions and exercises with answers
Showing questions 31–38 of 38.
A, B ⊆ U satisfy A ∩ B = ∅ and A ∪ B = U. Which equality must hold?Read the answer and worked solution →If A ∪ B = A ∩ B, which conclusion must be true?Read the answer and worked solution →A universe has 20 elements. A has 14 and B has 11. What is the full possible range for the number in A ∩ B?Read the answer and worked solution →Every element of A lies in B, and B ⊆ U. Complements use U. Which statement must hold?Read the answer and worked solution →A = {1, 2}, B = {2, 3}, C = {1, 3}. Each pair overlaps. What is A ∩ B ∩ C?Read the answer and worked solution →For x ∈ U and A, B ⊆ U, which condition is equivalent to x ∉ A ∪ B?Read the answer and worked solution →A, B ⊆ U and all complements use U. Which expression equals (A ∩ B)′?Read the answer and worked solution →U={1,2,3,4,5}, A={1,3}, (A∪B)′={4,5} and A∩B={3}. What is B?Read the answer and worked solution →
Worked practice questions
If A ∪ B = A ∩ B, which conclusion must be true?
- A = B
- A ∪ B = U
- A ∩ B = ∅
- A ≠ B
Show answer and solution
Correct answer: A. A = B
Any element in either set must also be common to both, so the sets contain exactly the same elements.
A universe has 20 elements. A has 14 and B has 11. What is the full possible range for the number in A ∩ B?
- 0 to 11
- 5 to 11
- 5 to 14
- 0 to 5
Show answer and solution
Correct answer: B. 5 to 11
At least 14 + 11 − 20 = 5 must overlap; at most all 11 elements of the smaller set can overlap, and every integer between is possible.
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