If A = {x : x = 2k, k ∈ Z} and B = {x : x = 3m, m ∈ Z}, then A ∩ B is the set of what?
Answer and explanation
Correct answer: Multiples of 6
Set A contains all integers divisible by 2, and set B contains all integers divisible by 3. An element of their intersection must satisfy both divisibility conditions at the same time. Since 2 and 3 are coprime, every integer divisible by both is divisible by their least common multiple, 6. Thus A ∩ B is the set of all integer multiples of 6, including 0 and negative multiples.
Frequently asked questions
What is the correct answer to this question?
Multiples of 6
Why is this the correct answer?
Set A contains all integers divisible by 2, and set B contains all integers divisible by 3. An element of their intersection must satisfy both divisibility conditions at the same time. Since 2 and 3 are coprime, every integer divisible by both is divisible by their least common multiple, 6. Thus A ∩ B is the set of all integer multiples of 6, including 0 and negative multiples.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
