If A \ B = B, which conclusion must be true?
Answer and explanation
Correct answer: B = ∅
By definition, A \ B contains elements of A that are not in B, so it is always disjoint from B. If A \ B is equal to B, then the same set must be disjoint from itself. The only set disjoint from itself is the empty set. Therefore B = ∅. The other options do not necessarily follow from the given equality.
Frequently asked questions
What is the correct answer to this question?
B = ∅
Why is this the correct answer?
By definition, A \ B contains elements of A that are not in B, so it is always disjoint from B. If A \ B is equal to B, then the same set must be disjoint from itself. The only set disjoint from itself is the empty set. Therefore B = ∅. The other options do not necessarily follow from the given equality.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Sets.
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