Please review Sections 2.2-2.4. Please give examples of how graphs are used in your life at home, business, investments, sports, etc.You may use the information in the textbook or talk about your own personal graphs. Please provide an example or two of those graphs by uploading a picture or siting a source.Then answer your classmates' posts and comment on their description.Please remember to use APA formatting if you use help from the textbook or a website. Try to use your own words!

Question 1: Consider the linear block cipher with block length n and alphabet {0, 1}. On the key space of matrices A ∈ {0, 1} (n,n) with det(A) ≡ 1 (mod 2), choose the uniform distribution. Show that this cryptosystem does not have perfect secrecy. (Use the definition of perfect secrecy, and find a counterexample with n = 2, for instance.) 2: Let n be a positive integer. A Latin square of order n is an n × n array L of the integers 1, 2, . . . , n such that every one of the n integers occurs exactly once in each row and each column of L. An example of a Latin square of order 3 is as follows:  1 2 3 3 1 2 2 3 1  . Given any Latin square L of order n, we can define the following cryptosystem: Take P = C = K = {1, 2, . . . , n}. For 1 ≤ i ≤ n, the encryption function Ei is defined to be Ei (j) = L(i, j). (Hence each row of L gives rise to one encryption function.) Give a complete proof that this Latin square cryptosystem achieves perfect secrecy. (Use Shannon’s theorem).If the question descriptions not clear enough, please check the picture file I posted.