A nonempty subset A of {1, 2, ... , n} is said to be relatively prime if gcd(A) = 1. Let f(n) and f_k(n) denote the number of relatively prime subsets and the number of relatively prime subsets of cardinality k of {1, 2, ... , n}, respectively. Let Φ(n) and Φ_k(n) denote the number of nonempty subsets and the number of subsets of cardinality k of {1, 2, ... , n} such that gcd(A) is relatively prime to n, respectively. In this paper, we obtain some properties of these functions.