Relative asymptotic growths

Indicate, for each pair of expressions $$(A, B)$$ in the table below, whether $$A$$ is $$O$$, $$o$$, $$\Omega$$, $$\omega$$, or $$\Theta$$ of $$B$$. Assume that $$k \ge 1, \epsilon > 0$$, and $$c > 1$$ are constants. Your answer should be in the form of the table with “yes” or “no” written in each box.

$\begin{array}{ccccccc} A & B & O & o & \Omega & \omega & \Theta \\ \hline \lg^k n & n^\epsilon & yes & yes & no & no & no \\ n^k & c^n & yes & yes & no & no & no \\ \sqrt n & n^{\sin n} & no & no & no & no & no \\ 2^n & 2^{n / 2} & no & no & yes & yes & no \\ n^{\lg c} & c^{\lg n} & yes & no & yes & no & yes \\ \lg(n!) & \lg(n^n) & yes & no & yes & no & yes \end{array}$