If n(A△B)=78 and n(A−B)=34, what is n(B−A)?
Answer and explanation
Correct answer: 44
The governing concept is the decomposition of symmetric difference: A△B = (A−B) ∪ (B−A). The two component sets are disjoint, so their cardinalities add. Hence 78 = 34 + n(B−A). Subtracting 34 from both sides gives n(B−A) = 78−34 = 44. Option A repeats the known first difference, option C repeats the total, and option D adds instead of subtracting. Therefore, option B is correct.
Frequently asked questions
What is the correct answer to this question?
44
Why is this the correct answer?
The governing concept is the decomposition of symmetric difference: A△B = (A−B) ∪ (B−A). The two component sets are disjoint, so their cardinalities add. Hence 78 = 34 + n(B−A). Subtracting 34 from both sides gives n(B−A) = 78−34 = 44. Option A repeats the known first difference, option C repeats the total, and option D adds instead of subtracting. Therefore, option B is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
