If A ∩ (B \ C) = ∅, which inclusion must be true?
Answer and explanation
Correct answer: A ∩ B ⊆ C
The condition A ∩ (B \ C) = ∅ says that no element can simultaneously belong to A and to B without belonging to C. Therefore, every element common to A and B must also be an element of C. Hence A ∩ B ⊆ C. The other options are stronger or unrelated statements and are not forced by the given condition.
Frequently asked questions
What is the correct answer to this question?
A ∩ B ⊆ C
Why is this the correct answer?
The condition A ∩ (B \ C) = ∅ says that no element can simultaneously belong to A and to B without belonging to C. Therefore, every element common to A and B must also be an element of C. Hence A ∩ B ⊆ C. The other options are stronger or unrelated statements and are not forced by the given condition.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
