If A = {x ∈ ℤ : x is divisible by 6} and B = {x ∈ ℤ : x is divisible by both 2 and 3}, which statement is correct?
Answer and explanation
Correct answer: A = B and both are infinite
If an integer is divisible by 6, then it can be written as 6k = 2(3k), so it is divisible by both 2 and 3. Conversely, if an integer is divisible by both 2 and 3, then because 2 and 3 are coprime, it is divisible by their product 6. Thus the two conditions describe exactly the same integers, so A = B. The multiples ..., −12, −6, 0, 6, 12, ... continue without end, making both sets infinite.
Frequently asked questions
What is the correct answer to this question?
A = B and both are infinite
Why is this the correct answer?
If an integer is divisible by 6, then it can be written as 6k = 2(3k), so it is divisible by both 2 and 3. Conversely, if an integer is divisible by both 2 and 3, then because 2 and 3 are coprime, it is divisible by their product 6. Thus the two conditions describe exactly the same integers, so A = B. The multiples ..., −12, −6, 0, 6, 12, ... continue without end, making both sets infinite.
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.
