Discrete Math

I attached the file for the proof.

WHAT YOU NEED TO DO

1. Create a series of graphics that could accompany the first paragraph illustrating each step in the proof. The illustrations should create a storyboard for the proof. The illustrations will give concrete examples of the concepts in the proof. That means your illustrations will have numerical values in the place of the arbitrary variables given in the proof. Each phrase of the proof should be illustrated. There may be some phrases that need more than on illustration to adequately explain the statement. Your illustrations should be labeled with the same notation that is used in the proof. Be sure to illustrate and for the digraph you used to illustrate the proof. You only need to illustrate the first paragraph of the proof. Make sure your illustrations are not too trivial. They should help the reader understand the logic of the proof.

– Note: The proof has two parts. Because the theorem is an “if and only if” statement, there are two sections of the proof. The first paragraph is one section of the proof. The second paragraph is the proof of the statement “If is a strict order, then has no positive length cycles.” The structure of the second part of the proof is a proof by contrapositive. You do not need to illustrate the second paragraph of the proof.

2. On a separate piece of paper, answer the following questions.

– What type of proof structure is used in the first paragraph of the proof?

– What is the value of in your illustration of the first paragraph?

– Why does a self-loop imply that cannot be anti-reflexive?

– What justifies the author’s statement that “Therefore is not a strict order”?