If A = {x : x ∈ N and x is a divisor of 15} and B = {1, 3, 5}, which relation is correct?
Answer and explanation
Correct answer: B ⊂ A and B ≠ A
The governing concept is the comparison of sets by listing their elements. The positive natural-number divisors of 15 are 1, 3, 5, and 15, so A = {1, 3, 5, 15}. Every element of B = {1, 3, 5} belongs to A, but A also contains 15. Therefore B is a proper subset of A, written B ⊂ A, and the sets are not equal. Thus option B is correct; option A ignores 15, while option D is false because the sets overlap.
Frequently asked questions
What is the correct answer to this question?
B ⊂ A and B ≠ A
Why is this the correct answer?
The governing concept is the comparison of sets by listing their elements. The positive natural-number divisors of 15 are 1, 3, 5, and 15, so A = {1, 3, 5, 15}. Every element of B = {1, 3, 5} belongs to A, but A also contains 15. Therefore B is a proper subset of A, written B ⊂ A, and the sets are not equal. Thus option B is correct; option A ignores 15, while option D is false because the sets overlap.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Equal sets and Subsets.
