I think that the first statement holds true in all cases; as from the definiton of Ω we can say that g(n) is not dominated by f(n)logn so we can say that f(n) is faster than g(n) since it must hold true for all n>n0. Hence A is faster than B if g(n)=Ω(f(n)logn.

I think that the first statement holds true in all cases; as from the definition of $\Omega$ we can say that $g(n)$ is not dominated by $f(n)\log n$ so we can say that $f(n)$ is faster than $g(n)$ since it must hold true for all $n>n_0$. Hence A is faster than B if $g(n)=\Omega(f(n)\log n)$.