If A ⊆ B and C ∩ B = ∅, then (A ∪ C) ∩ B is equal to which set?
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Answer and explanation
Correct answer: A
Distribute the intersection over the union: (A ∪ C) ∩ B = (A ∩ B) ∪ (C ∩ B). Since A ⊆ B, every element of A is already in B, so A ∩ B = A. The condition C ∩ B = ∅ removes the second part. Consequently, the expression becomes A ∪ ∅ = A. Hence option A is the only correct answer.
Frequently asked questions
What is the correct answer to this question?
A
Why is this the correct answer?
Distribute the intersection over the union: (A ∪ C) ∩ B = (A ∩ B) ∪ (C ∩ B). Since A ⊆ B, every element of A is already in B, so A ∩ B = A. The condition C ∩ B = ∅ removes the second part. Consequently, the expression becomes A ∪ ∅ = A. Hence option A is the only correct answer.
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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