If A = {1, 2, 3, 4} and B = {3, 4, 5, 6}, what is n(A − B) + n(B − A)?
Answer and explanation
Correct answer: 4
The difference A − B contains elements that are in A but not in B. Since 3 and 4 are common to both sets, A − B = {1, 2}, so n(A − B) = 2. Similarly, B − A contains elements in B but not in A, giving B − A = {5, 6} and n(B − A) = 2. Hence the required sum is 2 + 2 = 4. The value 2 counts only one directional difference, while 6 and 8 result from overcounting or using the wrong set formula.
Frequently asked questions
What is the correct answer to this question?
4
Why is this the correct answer?
The difference A − B contains elements that are in A but not in B. Since 3 and 4 are common to both sets, A − B = {1, 2}, so n(A − B) = 2. Similarly, B − A contains elements in B but not in A, giving B − A = {5, 6} and n(B − A) = 2. Hence the required sum is 2 + 2 = 4. The value 2 counts only one directional difference, while 6 and 8 result from overcounting or using the wrong set formula.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
