Let P $($n$)$ be the following statement:

The following sub$-$problems guide you through a proof by weak induction that P $($n$)$ holds

for all n in N$.$

$(1)(5$ points$)$ What is the statement P $(0)?$ Show that P $(0)$ is true, which

completes the base case.

$(2)(5$ points$)$ What is the inductive hypothesis?

$(3)(5$ points$)$ What do you need to prove in the inductive step?

$(4)(5$ points$)$ Complete the inductive step.