If A = {x ∈ ℕ : x is divisible by 6} and B = {x ∈ ℕ : 2 divides x and 3 divides x}, which statement is correct?
Answer and explanation
Correct answer: A = B, and both are infinite sets
A natural number divisible by both 2 and 3 is divisible by their least common multiple, 6. Conversely, every multiple of 6 is divisible by both 2 and 3. Thus A and B contain exactly the same numbers: 6, 12, 18, 24, and so on. Since there are endlessly many multiples of 6, both sets are infinite and A = B.
Frequently asked questions
What is the correct answer to this question?
A = B, and both are infinite sets
Why is this the correct answer?
A natural number divisible by both 2 and 3 is divisible by their least common multiple, 6. Conversely, every multiple of 6 is divisible by both 2 and 3. Thus A and B contain exactly the same numbers: 6, 12, 18, 24, and so on. Since there are endlessly many multiples of 6, both sets are infinite and 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.
