The set S contains some real numbers, according to the following three rules. (i) is in S. (ii) If is in S, where is written in lowest terms (that is, a and I have highest common factor 1), then is in S. b 2a (iii) If andare in S, where they are written in lowest terms, then is in S. b+d These rules are exhaustive: if these rules do not imply that a number is in S, then that number is not in S. Can you describe which numbers are in S? For example, by (i), is in S. By (ii), since is in S, is in S. Since both andare in S, (iii) tells us 1+1 is in S. 1+2