If A = {x : x ∈ N, x < 8} and B = {x : x ∈ N, 4 < x < 10}, what is A \ B?
Answer and explanation
Correct answer: {1, 2, 3, 4}
Taking N as the positive natural numbers, A = {1, 2, 3, 4, 5, 6, 7} because x < 8. The conditions 4 < x < 10 give B = {5, 6, 7, 8, 9}. Set difference A \ B keeps only the elements of A that do not occur in B. Removing 5, 6, and 7 from A leaves {1, 2, 3, 4}. Hence, option A is correct. The strict inequalities exclude 4 from B and 10 from consideration.
Frequently asked questions
What is the correct answer to this question?
{1, 2, 3, 4}
Why is this the correct answer?
Taking N as the positive natural numbers, A = {1, 2, 3, 4, 5, 6, 7} because x < 8. The conditions 4 < x < 10 give B = {5, 6, 7, 8, 9}. Set difference A \ B keeps only the elements of A that do not occur in B. Removing 5, 6, and 7 from A leaves {1, 2, 3, 4}. Hence, option A is correct. The strict inequalities exclude 4 from B and 10 from consideration.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
