Let $f(n)$ and $g(n)$ be asymptotically positive functions. Prove or disprove each of the following conjectures.

$f(n)=O(g(n))$ implies $g(n)=O(f(n))$

$f(n)+g(n)=(min(f(n),g(n)))$

$f(n)=(f(\frac{n}{2}))$

$f(n)=O(g(n))$ implies $g(n)=(f(n))$

$f(n)=O((f(n){)}^2)$