If A = {1, 2, 3, 4, 5, 6}, B = {2, 4, 6, 8}, and C = {1, 4, 6}, what is A − (B ∩ C)?
Answer and explanation
Correct answer: {1, 2, 3, 5}
Evaluate the parentheses first. The elements common to B = {2, 4, 6, 8} and C = {1, 4, 6} are B ∩ C = {4, 6}. Set difference A − (B ∩ C) means remove 4 and 6 from A. Starting with A = {1, 2, 3, 4, 5, 6}, the remaining elements are {1, 2, 3, 5}. Thus option A is correct; option B is the removed intersection, not the difference.
Frequently asked questions
What is the correct answer to this question?
{1, 2, 3, 5}
Why is this the correct answer?
Evaluate the parentheses first. The elements common to B = {2, 4, 6, 8} and C = {1, 4, 6} are B ∩ C = {4, 6}. Set difference A − (B ∩ C) means remove 4 and 6 from A. Starting with A = {1, 2, 3, 4, 5, 6}, the remaining elements are {1, 2, 3, 5}. Thus option A is correct; option B is the removed intersection, not the difference.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
