Question $1$: Consider the following segment of code. Assume that i$,$ x$,$ and n are integers, and

that n is non$-$negative

i $0$

x $5$

while i $<$ n do

x $2$x

i $$i $+1$

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$.$