If A ∩ B′ = A, which of the following conclusions must be true?
Answer and explanation
Correct answer: A ⊆ B′
The equality A ∩ B′ = A says that intersecting A with B′ removes no element from A. Therefore every element of A must already belong to B′, which is precisely the statement A ⊆ B′. Equivalently, no element of A belongs to B. The equality does not imply that B is contained in A, that A and B are equal, or that their union is the universal set. Thus option A is the only necessary conclusion.
Frequently asked questions
What is the correct answer to this question?
A ⊆ B′
Why is this the correct answer?
The equality A ∩ B′ = A says that intersecting A with B′ removes no element from A. Therefore every element of A must already belong to B′, which is precisely the statement A ⊆ B′. Equivalently, no element of A belongs to B. The equality does not imply that B is contained in A, that A and B are equal, or that their union is the universal set. Thus option A is the only necessary conclusion.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Sets.
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