If A = {x : x ∈ ℕ, x ≤ 15} and B = {x : x ∈ ℕ, x is odd, x ≤ 15}, what is A − B?
Answer and explanation
Correct answer: {2, 4, 6, 8, 10, 12, 14}
A contains all natural numbers up to 15, while B contains the odd natural numbers up to 15. Subtracting B from A removes 1, 3, 5, 7, 9, 11, 13, and 15. The elements left in A are precisely the even natural numbers up to 15: {2, 4, 6, 8, 10, 12, 14}. Therefore option B is correct. Option A is B itself, option C incorrectly includes 16, which is greater than 15, and option D would mean every element of A were odd.
Frequently asked questions
What is the correct answer to this question?
{2, 4, 6, 8, 10, 12, 14}
Why is this the correct answer?
A contains all natural numbers up to 15, while B contains the odd natural numbers up to 15. Subtracting B from A removes 1, 3, 5, 7, 9, 11, 13, and 15. The elements left in A are precisely the even natural numbers up to 15: {2, 4, 6, 8, 10, 12, 14}. Therefore option B is correct. Option A is B itself, option C incorrectly includes 16, which is greater than 15, and option D would mean every element of A were odd.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
