Question

Write the set \({\frac{1}{2}, \frac{2}{3}, \frac{3}{4}, \frac{4}{5}, \frac{5}{6}}\) in set builder form.

(a) {x: \(x=\frac{n}{n+1}\) where n is a natural number less than 6}

(b) {x: \(x=\frac{n+1}{n+2}\) where n is a natural number less than 6}

(c) {x: \(x=\frac{n+1}{n}\) where n is a natural number less than 6}

(d) {x: \(x=\frac{n}{n+1}\) where n is a natural number less than 5}

The question was posed to me in an interview.

My question comes from Sets and their Representations in portion Sets of Mathematics – Class 11

Answer 1

The correct option is (a) {x: \(x=\frac{n}{n+1}\) where n is a natural number less than 6}

Explanation: Since denominator is one more than numerator and only 5 terms are present.                                     So, the above set can be written as {x : \(x=\frac{n}{n+1}\) where n is a natural number less than 6}.