Discrete Math help

5. (25 points) (This question has 3 parts) (a) (5 points) Let S,NEN. Using the notation we've used in class, write a simple loop for computing SN. (Do not assume you can use an exponentiation operator, Use only the + operator, and a while loop. Create whatever variables you need.) (649 (b) (12 points) Provide a loop invariant, p, for your code, and prove its correctness by showing that p^ B{S}p is a good Hoare triple. (c) (8 points) (p ^ B){S}p p{while B do S}(P1-B) Use the While loop inference rule above, and the fact that p is a good loop invariant, to prove that your code outputs SN