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MM250 Unit 2 Assignment




Question;Unit 2: Boolean Algebra ? AssignmentTotal points for Assignment: 35 points.Assignments must be submitted as a Microsoft Word document and uploaded to the Dropbox for Unit2.All Assignments are due by Tuesday at 11:59 PM ET of the assigned Unit.NOTE: Assignment problems should not be posted to the Discussion threads. Questions on theAssignment problems should be addressed to the instructor by sending an email or by attendingoffice hours.You must show your work on all problems. If a problem is worth 2 points and you only show theanswer, then you will receive only 1 point credit. If you use a calculator or online website, give thesource and tell me exactly what you provided as input. For example, if you used Excel to compute16 * 16, tell me ?I typed =16*16 into Excel and got 256. You may type your answer right into thisdocument.Since this assignment is somewhat unusual in that there are no computations, you will need tocompose an explanation of your answer. Pretend you are explaining your solution to your friend(we?ll assume that he/she doesn?t know anything about Boolean Algebra). You are free to usewords instead of the symbol in your explanations (e.g. ?and? instead of?, ?arrow? instead of?)Part I. Basic Computations1. (4 points ? 2 points each) Let p, q, and r represent the following simple statements:p: The temperature outside is hotq: The air conditioner in my house is workingr: The temperature in my house feels warmWrite each compound statement in it?s symbolic form, using p, q, and r from above:a.The air conditioner in my house is not working and the temperature in my house feelswarm.Answer:Explanation:b.If the temperature outside is hot or the air conditioner in my house is not working thenthe temperature in my house feels warm.Answer:Explanation:Copyright 2010 ? Kaplan University ? All Rights Reserved1 | P a g e2.(4 points ? 2 points each) Let p, q, and r represent the following simple statements:p: The temperature is above 90 degrees.q: I am not workingr: We will go swimmingWrite each compound statement in words, using p, q, and r from above:a.p? (q? r)Answer:Explanation:b.(~q? ~p)? ~rAnswer:Explanation:3.(2 points) The column graph below shows the monthly sales for some organization, brokendown by region.Let:p:q:r:NE region had higher monthly sales than the SW regionNE region had higher monthly sales than the SE regionSE region monthly sales are equal to the SW monthly salesDetermine the truth value of the following statement, then explain in words how you know.(p? ~q)? rAnswer:Explanation:Copyright 2010 ? Kaplan University ? All Rights Reserved2 | P a g e4.(2 points) Complete the following truth table for the logical statement [(~p? q)??r]pTTTTFFFFqTTFFTTFFrTFTFTFTF~p?r~p? q[(~p? q)??r]Explanation: No explanation needed for this problem.5.Determine whether the following statements are equivalent or not, (p? r)? ~q with p? (r? ~q),using the following truth table.(2 points) Complete the following truth tablepTTTTFFFFqTTFFTTFFrTFTFTFTF~q(p? r)(r? ~q)(1 point) Conclusion: These statements are (pick one)EQUIVALENT(p? r)? ~qp? (r? ~q)EQUIVALENTNOTAnswer:Copyright 2010 ? Kaplan University ? All Rights Reserved3 | P a g ePart II. Case StudyThe case of the Noon-time robberyThis week Patty Madeye will be investigating a bank robbery.The Main Street bank was robbed at exactly 12 noon on Tuesdayby either 3 or 4 men. The group escaped in a getaway car,which has not been recovered.From the police investigators here?s what we will have learnedabout the case:-All the robbers appeared to be men, although they may havebeen attempting to disguise their appearances.There were either 3 or 4 robbers - we?re not sure due toconflicting eye-witness accountsThe getaway car was a late-model 4-door sedan that was adark color (either blue, black or dark green)Task #1: (5 points ? 1 point each) In the first scene of the ?Patty Madeye Mysteries? this week, Pattywill be told all the known information by the police investigators who responded to the emergency callat 12:05pm on Tuesday. This will consist of the separate eye-witness accounts the policeinvestigators collected as well as police conjectures.She likes to record her notes using simple logic statements. Use the following 4 statements toexpress the given compound statement given by each eye-witness and the police investigators:p:There were 4 bank robbersq:All the bank robbers were menr:One robber had a ponytails:The getaway car was blueYou may use AND, OR, NOT, XOR, and ARROW instead of the logic symbols used in the notes, butbe sure to use parenthases as needed to represent precedence. p AND q ARROW r is not thesame thing asp AND (q ARROW r).a.One robber had a ponytail or all the bank robbers were men, but there were only 3 bankrobbersAnswer:Explanation:b.There were 4 bank robbers, but all the bank robbers were men and one robber had aponytailAnswer:Explanation:Copyright 2010 ? Kaplan University ? All Rights Reserved4 | P a g ec.If there were 4 bank robbers and one of the robbers had a ponytail, then all the bankrobbers were menAnswer:Evaluation:d.If the getaway car was blue then one robber had a ponytail and there were not 4 bankrobbersAnswer:Explanation:e.Either the getaway car was blue or one robber had a ponytail (but not botH), and all thebank rubbers were men.Answer:Explanation:Task #2: (5 points) The writers can?t decide who the leader of the bank robbers should be. Theythink that the leader should either be a female (disguised as a man) or someone with black hair (butnot both), and the leader should also be tall (over 5? 10?).Since you have studied logic, the writers ask you to compose a truth table to figure out all thecombinations of these three characteristics (gender, hair color, short/tall). Given these 3 simplestatements, determine the correct compound statement for the condition stated above, thendetermine a truth table for that statement.p:q:r:The leader is a femaleThe leader has black hairThe leader is tall (over 5? 10?)pqrTTTTTFTFTTFFFTTFTFFFTFFFCopyright 2010 ? Kaplan University ? All Rights Reserved5 | P a g eTask #3 (10 points) The writers and actors have finally agreed on the characteristics for the leader ofthe bank robbers. Based on the results of focus groups and extensive research, they have tried allthe following combinations for the following three statementsp:q:r:The leader has black hairThe leader is femaleThe leader is tall (over 5? 10?)The focus groups seemed to zoom in on one particular combination, as shown in this truth table:pqrTTFTTFFTFTFTFFTFTTFFTFFFFTFFFFFTUnfortunately, thispart was obscuredby a water stain.You are given the descriptions for the six actors/actresses under consideration.Actor A- male- 6? tall- baldActress B- female- 5? 5?- black hairActor C- male- 5? 5?- black hairActor D- male- 5?5?- red hairActor E- male- 6?- black hairActor F- male- 5?6?- baldUsing the evidence from above and what you have learned about logic, explain in a well-structuredessay which person should play the part of the leader of the bank robbers. Your answer shouldinclude what you think the obscured logic statement is (from the top of the column in the truth table).You will need to recreate the missing colunm of the truth table that produced the above results, thenevaluate the truth value of that statement using each of the above actors. Answers will vary.Answer:Requirements- Write your essay in this document ? do not save it in a separate file.- You must clearly state your position in 2-3 well-structured paragraphs using proper grammar,spelling, and sentence structure.- This is not an ?opinion? question ? you must offer evidence from the truth table to support yourpositionCopyright 2010 ? Kaplan University ? All Rights Reserved6 | P a g e


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