If A ∩ B ⊆ A \ C, which statement must be true?
Answer and explanation
Correct answer: A ∩ B ∩ C = ∅
Every element of A ∩ B is, by the given inclusion, an element of A \ C. Membership in A \ C means being in A but not being in C. Therefore, no element of A ∩ B can belong to C. Equivalently, the intersection of A ∩ B with C is empty, so A ∩ B ∩ C = ∅. The other statements do not follow from the given inclusion.
Frequently asked questions
What is the correct answer to this question?
A ∩ B ∩ C = ∅
Why is this the correct answer?
Every element of A ∩ B is, by the given inclusion, an element of A \ C. Membership in A \ C means being in A but not being in C. Therefore, no element of A ∩ B can belong to C. Equivalently, the intersection of A ∩ B with C is empty, so A ∩ B ∩ C = ∅. The other statements do not follow from the given inclusion.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
