If A = {1, 2, 3, 4, 5, 6}, B = {2, 3, 5, 7}, and C = {3, 5, 8}, what is A ∩ (B \ C)?
Answer and explanation
Correct answer: {2}
The governing concepts are set difference and intersection. In B \ C, remove from B every element that also occurs in C. Since 3 and 5 occur in C, B \ C = {2, 7}. Now intersect this result with A, retaining only elements common to both sets. The element 2 belongs to A, but 7 does not. Therefore A ∩ (B \ C) = {2}, so option A is correct; option D incorrectly keeps 7.
Frequently asked questions
What is the correct answer to this question?
{2}
Why is this the correct answer?
The governing concepts are set difference and intersection. In B \ C, remove from B every element that also occurs in C. Since 3 and 5 occur in C, B \ C = {2, 7}. Now intersect this result with A, retaining only elements common to both sets. The element 2 belongs to A, but 7 does not. Therefore A ∩ (B \ C) = {2}, so option A is correct; option D incorrectly keeps 7.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
