If A ∪ B = B and A ∩ C = C, which statement must be true?
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Answer and explanation
Correct answer: C ⊆ B
The equality A ∪ B = B means that adding every element of A to B does not enlarge B, so every element of A is already in B; therefore A ⊆ B. Similarly, A ∩ C = C means every element of C belongs to A, so C ⊆ A. By transitivity of subset relation, C ⊆ A ⊆ B, and hence C ⊆ B.
Frequently asked questions
What is the correct answer to this question?
C ⊆ B
Why is this the correct answer?
The equality A ∪ B = B means that adding every element of A to B does not enlarge B, so every element of A is already in B; therefore A ⊆ B. Similarly, A ∩ C = C means every element of C belongs to A, so C ⊆ A. By transitivity of subset relation, C ⊆ A ⊆ B, and hence C ⊆ B.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
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