What type of set is A = {x : x ∈ N, x is divisible by both 13 and 17}?
Answer and explanation
Correct answer: Infinite set
A natural number divisible by both 13 and 17 must be a multiple of their product, 13 × 17 = 221, because the numbers are relatively prime. Thus A contains 221, 442, 663, 884, and so on. Multiplying 221 by every positive natural number produces another member, with no upper bound. Hence the set has infinitely many elements, so option C is correct.
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 13 and 17 must be a multiple of their product, 13 × 17 = 221, because the numbers are relatively prime. Thus A contains 221, 442, 663, 884, and so on. Multiplying 221 by every positive natural number produces another member, with no upper bound. Hence the set has infinitely many elements, so option C is correct.
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.
