Suppose f(n) = O(s(n)), and g(n) = O(r(n)). All functions should have Z0 as their domain and codomain. Prove or disprove (by giving a counterexample) the following claims:

(a) f(n) g(n) = O(s(n) r(n))

(b) f(n) / g(n) = O(s(n) / r(n))

(c) if g(n) = O(f (n)), then f (n) + g(n) = O(s(n))

(d) if r(n) = O(s(n)), then g(n) = O(f(n))