If A ⊆ B ⊆ C, then what is A ∩ B ∩ C equal to?
Answer and explanation
Correct answer: A
Since A⊆B and A⊆C, every element of A belongs to all three sets. Conversely, an element in A∩B∩C must certainly belong to A. Thus the intersection cannot contain anything outside A and contains every element of A, so A∩B∩C=A. B and C may contain additional elements, while C−A contains elements specifically excluded from A.
Frequently asked questions
What is the correct answer to this question?
A
Why is this the correct answer?
Since A⊆B and A⊆C, every element of A belongs to all three sets. Conversely, an element in A∩B∩C must certainly belong to A. Thus the intersection cannot contain anything outside A and contains every element of A, so A∩B∩C=A. B and C may contain additional elements, while C−A contains elements specifically excluded from A.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Equal sets and Subsets.
