If A ⊆ B ⊆ U, which statement is always true?
Answer and explanation
Correct answer: B′ ⊆ A′
Taking complements reverses the direction of set inclusion. If A is a subset of B, every element outside B is certainly outside A, because A contains no element that is not in B. Therefore U − B is a subset of U − A, which is written as B′ ⊆ A′. Equality is not guaranteed because A and B may be different sets. Thus option A is always true.
Frequently asked questions
What is the correct answer to this question?
B′ ⊆ A′
Why is this the correct answer?
Taking complements reverses the direction of set inclusion. If A is a subset of B, every element outside B is certainly outside A, because A contains no element that is not in B. Therefore U − B is a subset of U − A, which is written as B′ ⊆ A′. Equality is not guaranteed because A and B may be different sets. Thus option A is always true.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Sets.
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