Consider the following definition of Fibonacci numbers:

F$($n$)=$

$$

$$

$$

$0$ if n $=0$

$1$ if n $=1$

F$($n $1)+$ F$($n $2)$ if n $>=2$

a$.$ Give the set of all natural numbers q for which F$($q$)>=1\mathrm{.}6$

q$2$

$.$ Justify briefly.

b$.$ Does your answer to a imply the following assertion: $$c$,$ n$0>0,$ such that $0<=$ c $1\mathrm{.}6$

n $<=$ F$($n$),$

$$n $>=$ n$0.$ Explain briefly.

c$.$ Consider the following recursive implementation of function F$($n$)$