List of top Quantitative Ability and Data Interpretation Questions on Rational or Irrational Numbers

Let \(S\) be the set of rational numbers with the following properties:
(i) \(\dfrac{1}{2} \in S\);
(ii) If \(x \in S\), then both \(\dfrac{1}{x+1} \in S\) and \(\dfrac{x}{x+1} \in S\).
Which of the following is true?