WHIN WORKTING OUT YOUR SOLUMONS, SHOW ALL RMLUVANI WORK.

$(7$ pts total$)$ Prove $($by using the definitions of the notations involved$)$ or disprove $($by giving a specific counterexample$)$ the following assertions.

a$.o.(ag(n))=o.(g(n)),$ where $>0.$

b$.$ For any two nonnegative functions $t(n)$ and $g(n)$ defined on the set of nonnegative integers, either $t(n)inO(g(n)),$ or $t(n)in(g(n)),$ or both.

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