Question

Which one of the following is the correct representation of set A = {1,3,5,7….} in set builder form?

(a) {x: x = 2n where n ∈ N}

(b) {x: x = n^2-1 where n ∈ N}

(c) {x: x = 2n+1 where n ∈ N}

(d) {x: x = 2n-1 where n ∈ N}

I have been asked this question in final exam.

The question is from Sets and their Representations in portion Sets of Mathematics – Class 11

Answer 1

Right option is (d) {x: x = 2n-1 where n ∈ N}

Easy explanation: The given sequence is an odd number sequence of the format 2n+1 or 2n-1, but since n is given as a natural number so 2n+1 is not valid as 0 is not a natural number hence 2n-1 is the correct answer.