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)