If n(A − B) = 29 and n(B − A) = 17, what is n(A △ B)?
Answer and explanation
Correct answer: 46
The governing concept is symmetric difference. The set A △ B contains elements belonging to exactly one of A or B, so A △ B = (A − B) ∪ (B − A). These two difference sets cannot overlap; hence their cardinalities are added. Thus n(A △ B) = 29 + 17 = 46. Options C and D represent only one part, and option A subtracts the parts incorrectly. Therefore, option B is correct.
Frequently asked questions
What is the correct answer to this question?
46
Why is this the correct answer?
The governing concept is symmetric difference. The set A △ B contains elements belonging to exactly one of A or B, so A △ B = (A − B) ∪ (B − A). These two difference sets cannot overlap; hence their cardinalities are added. Thus n(A △ B) = 29 + 17 = 46. Options C and D represent only one part, and option A subtracts the parts incorrectly. Therefore, option B is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
