What is the nature of A = {x ∈ N : x is divisible by 2 and by 3}?
Answer and explanation
Correct answer: Infinite set
A natural number divisible by both 2 and 3 is divisible by their least common multiple, 6. Hence A = {6, 12, 18, 24, ...}. This sequence continues without an end because for every member 6n, the next member 6(n + 1) is also a natural number satisfying both conditions. Therefore A is infinite, not merely the singleton {6}.
Frequently asked questions
What is the correct answer to this question?
Infinite set
Why is this the correct answer?
A natural number divisible by both 2 and 3 is divisible by their least common multiple, 6. Hence A = {6, 12, 18, 24, ...}. This sequence continues without an end because for every member 6n, the next member 6(n + 1) is also a natural number satisfying both conditions. Therefore A is infinite, not merely the singleton {6}.
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.
