If A = {x ∈ ℕ : x is a divisor of 15} and B = {x ∈ ℕ : x < 15 and x divides 15}, which statement is correct?
Answer and explanation
Correct answer: A ≠ B, because 15 ∈ A but 15 ∉ B
The positive natural-number divisors of 15 are 1, 3, 5, and 15, so A = {1, 3, 5, 15}. Set B requires the divisor to be less than 15, so it contains only {1, 3, 5}; the divisor 15 itself is excluded. Thus 15 belongs to A but not to B. Since two sets cannot be equal when one contains an element absent from the other, A ≠ B.
Frequently asked questions
What is the correct answer to this question?
A ≠ B, because 15 ∈ A but 15 ∉ B
Why is this the correct answer?
The positive natural-number divisors of 15 are 1, 3, 5, and 15, so A = {1, 3, 5, 15}. Set B requires the divisor to be less than 15, so it contains only {1, 3, 5}; the divisor 15 itself is excluded. Thus 15 belongs to A but not to B. Since two sets cannot be equal when one contains an element absent from the other, A ≠ B.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: The Empty Set, Finite and Infinite Sets, Equal Sets.
