Question $2$: Consider the following segment of code. Assume that i$,$ x$,$ and n are integers, and

n $1.$

i $1$

f $1$

while i $<$ n do

i $$i $+1$

f $$f $$i

end while

$1.$ State a loop invariant. For full credit, it must be a non$-$trivial invariant which includes

information about both i and x$.$

$2.$ Prove the loop invariant you stated in part $($a$)$

$3.$ Use the $$while loop$$ inference rule to make a claim about the program$$s output x