Suppose we have the following 3 functions
f(n), g(n), h(n)
such that f(n) = Omega(g(n)) and g(n) = Omega(h(n)). Must it be the case that f(n) = Omega(h(n))? Explain why or give a counterexample.
My attempt:
f(n)>= c1g(n) for all n>n1
g(n)>=c2 h(n) for all n>n2
So, f(n)>=c1 c2 for all n>min(n1,n2)