” 写作CIT 592课程程序、Python，Java，c/c++程序CIT 592 Spring 2020 Homework 1YOUR NAME HEREYOUR PENN EMAIL HERE1. [10 pts] Jack and Jill want to rent separate apartments on the third floor of a new buildingby the river. The building has nine apartments available, numbered 301, 302,. . . , 309. Theodd-numbered apartments have a river view, and the even-numbered apartments do not. Jillwill only rent an apartment with a river view, and Jack does not care about the view.How many distinct possibilities exist for the pair of apartments they end up renting?Solution.YOUR SOLUTION HERE2. [10 pts](a) A number n N is called perfect if the sum of all of ns factors other than n itself is equalto n. For Example, 6 is perfect because its factors are 1, 2, 3, and 6, and 1 + 2 + 3 = 6.Prove that there are no perfect prime numbers.(b) Let m, n Z+, and suppose that m is a factor of both n and n + 1. Prove that m = 1.Solution.(a) YOUR SOLUTION HERE(b) YOUR SOLUTION HEREHomework 1 CIT 592 23. [10 pts] n 2 distinguishable Hogwarts students participate in Professor Snapes experiment.Each student is given one of three concoctions: potion A, or potion B, or a mixture of the two.Snape makes sure to give a different concoction to each of Harry and Hermione. In how manydistinct ways could Snape have distributed his concoctions?Solution.YOUR SOLUTION HERE4. [12 pts] Prove that for all odd integers x and y we have 8 | x2 y2 写作CIT 592课程作业、Python，Java，c/c++程序Solution.YOUR SOLUTION HERE5. [8 pts](a) Give an example of three distinct (no two are the same), nonempty sets A, B, C such that there are elements that are common to A and B; every element of A that is also in B must also be in C; there are elements in A that are not in C.(b) Let A be a finite set such that {} A and {} A and |A| = 2. List all the subsets ofA. Justify your answer.(c) Consider the sets A = {1, 2, 3}, B = {x2| x A}, and also C = {x+y | x B and y A}.List the elements of A C. Show your work.(d) Give examples Of three sets A, B, C {1, 2, 3, 4, 5, 6, 7} such that A and B are disjoint,A \ C = {1, 3, 7}, B C = {2, 4, 5}, |A| = 5, and B \ C 6= . Show your work.Solution.(a) YOUR SOLUTION HERE(b) YOUR SOLUTION HERE(c) YOUR SOLUTION HEREHomework 1 CIT 592 3(d) YOUR SOLUTION HERE6. [10 pts] Let A = {2, 3}, B = {3, 4}, C = {2, 3, 4}, and S = A 2B2C. Answer each of thefollowing questions. Explain your answers.(a) (2, {(2, {2})}) S ?(b) (2, {(3, {4})}) S ?(c) (2, {({4}, 4)}) S ?Solution.(a) YOUR SOLUTION HERE(b) YOUR SOLUTION HERE(c) YOUR SOLUTION HERE7. [6 pts] EXTRA CREDIT CHALLENGE PROBLEMWe have a bag filled with 110 marbles, where 55 of them are blue and 55 of them are red. Everyturn, We remove 2 marbles from the bag. If the Two marbles are of the same color, we removethe two marbles but add a red marble into the bag. If the two marbles are of different colors,we remove the two marbles and add a blue marble into the bag.What is the color of the last marble in the bag?Solution.YOUR SOLUTION HERE如有需要，请加QQ：99515681 或邮箱：99515681@qq.com
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