If A ∩ (B \ C) = A ∩ B, which conclusion must be true?
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Answer and explanation
Correct answer: A ∩ B ∩ C = ∅
The set B \ C contains elements of B that are not in C. Therefore, A ∩ (B \ C) cannot contain any element of C. Since this set is equal to A ∩ B, no element common to A and B can belong to C. Hence (A ∩ B) ∩ C is empty, or A ∩ B ∩ C = ∅. Thus option A is the necessary conclusion.
Frequently asked questions
What is the correct answer to this question?
A ∩ B ∩ C = ∅
Why is this the correct answer?
The set B \ C contains elements of B that are not in C. Therefore, A ∩ (B \ C) cannot contain any element of C. Since this set is equal to A ∩ B, no element common to A and B can belong to C. Hence (A ∩ B) ∩ C is empty, or A ∩ B ∩ C = ∅. Thus option A is the necessary conclusion.
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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