If A = {1, 2, 3, 4, 5}, B = {2, 3, 6}, and C = {3, 4, 7}, what is the value of A − (B ∩ C)?
Answer and explanation
Correct answer: {1, 2, 4, 5}
To evaluate A − (B ∩ C), first calculate the operation inside the parentheses. The elements common to B = {2, 3, 6} and C = {3, 4, 7} form B ∩ C = {3}. Set difference A − {3} means retaining every element of A that is not 3. Removing 3 from A = {1, 2, 3, 4, 5} gives {1, 2, 4, 5}. Therefore, option A is correct. The order of operations matters: find the intersection first, then perform the difference.
Frequently asked questions
What is the correct answer to this question?
{1, 2, 4, 5}
Why is this the correct answer?
To evaluate A − (B ∩ C), first calculate the operation inside the parentheses. The elements common to B = {2, 3, 6} and C = {3, 4, 7} form B ∩ C = {3}. Set difference A − {3} means retaining every element of A that is not 3. Removing 3 from A = {1, 2, 3, 4, 5} gives {1, 2, 4, 5}. Therefore, option A is correct. The order of operations matters: find the intersection first, then perform 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).
