In a Venn diagram, A − (B ∪ C) is equal to what?
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Answer and explanation
Correct answer: A ∩ B' ∩ C'
The difference A − (B ∪ C) contains elements that belong to A but do not belong to the union B ∪ C. Not belonging to B ∪ C means being outside both B and C, which is represented by B' ∩ C'. Thus A − (B ∪ C) = A ∩ (B ∪ C)' = A ∩ B' ∩ C' by De Morgan’s law. Option A is correct.
Frequently asked questions
What is the correct answer to this question?
A ∩ B' ∩ C'
Why is this the correct answer?
The difference A − (B ∪ C) contains elements that belong to A but do not belong to the union B ∪ C. Not belonging to B ∪ C means being outside both B and C, which is represented by B' ∩ C'. Thus A − (B ∪ C) = A ∩ (B ∪ C)' = A ∩ B' ∩ C' by De Morgan’s law. Option A is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
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