If A \ (B ∩ C) = ∅, which statement must be true?
Answer and explanation
Correct answer: A ⊆ B ∩ C
For any sets X and Y, X \ Y = ∅ exactly when every element of X belongs to Y, which is equivalent to X ⊆ Y. Applying this fact with X = A and Y = B ∩ C, the given condition implies A ⊆ B ∩ C. It does not require B ∩ C to be contained in A, nor does it imply disjointness or the stated union equality.
Frequently asked questions
What is the correct answer to this question?
A ⊆ B ∩ C
Why is this the correct answer?
For any sets X and Y, X \ Y = ∅ exactly when every element of X belongs to Y, which is equivalent to X ⊆ Y. Applying this fact with X = A and Y = B ∩ C, the given condition implies A ⊆ B ∩ C. It does not require B ∩ C to be contained in A, nor does it imply disjointness or the stated union equality.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
