If S₁ = {x : x ∈ ℕ, x leaves remainder 2 when divided by 5}, what type of set is S₁?
Answer and explanation
Correct answer: Infinite set
A natural number leaves remainder 2 on division by 5 precisely when it has the form 5k + 2, where k is a nonnegative integer (with the usual convention that natural numbers include positive values). The resulting members begin 2, 7, 12, 17, 22, and continue indefinitely by adding 5. There is no upper bound on k, so the set has infinitely many elements and is therefore infinite.
Frequently asked questions
What is the correct answer to this question?
Infinite set
Why is this the correct answer?
A natural number leaves remainder 2 on division by 5 precisely when it has the form 5k + 2, where k is a nonnegative integer (with the usual convention that natural numbers include positive values). The resulting members begin 2, 7, 12, 17, 22, and continue indefinitely by adding 5. There is no upper bound on k, so the set has infinitely many elements and is therefore 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.
