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MM250 Unit 2 Assignment-Boolean Algebra

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Question;Unit 2: Boolean Algebra - Assignment;Total;points for Assignment: 35 points.;Assignments;must be submitted as a Microsoft Word document and uploaded to the Dropbox for;Unit 2.;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 the Assignment problems should;be addressed to the instructor by sending an email or by attending office;hours.;You must show your;work on all problems. If a problem is worth;2 points and you only show the answer, then you will receive only 1 point;credit. If you use a calculator or online website;give the source and tell me exactly what you provided as input. For example, if you used Excel to compute 16;* 16, tell me ?I typed =16*16 into Excel and got 256. You may type your answer right into this;document.;Since;this assignment is somewhat unusual in that there are no computations, you will;need to compose 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 use words instead of thesymbol in your explanations;(e.g. ?and? instead of?, ?arrow? instead of?);Part I. Basic Computations;1. (4 points ? 2 points each) Let p, q, and r represent the following simple;statements;p: The temperature outside is hot;q: The air conditioner in my house is working;r: The temperature in my house feels warm;Write 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 feels warm.;Answer;Explanation;b. If;the temperature outside is hot or the air conditioner in my house is not;working then the temperature in my house feels warm.;Answer;Explanation;2. (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 working;r: We will go swimming;Write each compound statement in;words, using p, q, and r from above;a. p?;(q? r);Answer;Explanation;b. (~q;? ~p)? ~r;Answer;Explanation;3. (2 points) The column graph below shows the monthly;sales for some organization, broken down by region.;Let: p: NE region had higher monthly sales than;the SW region;q: NE region had higher monthly sales than;the SE region;r: SE region monthly sales are equal to;the SW monthly sales;Determine;the truth value of the following statement, then explain in words how you know.;(p?;~q)? r;Answer;Explanation;4. (2 points) Complete the following truth table for the;logical statement [(~p?;q)?~r];p;q;r;~r;~p;~p? q;[(~p? q)?~r];T;T;T;T;T;F;T;F;T;T;F;F;F;T;T;F;T;F;F;F;T;F;F;F;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 table;p;q;r;~q;(p? r);(r? ~q);(p? r)? ~q;p? (r? ~q);T;T;T;T;T;F;T;F;T;T;F;F;F;T;T;F;T;F;F;F;T;F;F;F;(1 point) Conclusion: These statements are (pick one) EQUIVALENT NOT EQUIVALENT;Answer;Part II. Case Study The case of the Noon-time robbery;This week Patty Madeye will be investigating a bank;robbery. The Main Street bank was;robbed at exactly 12 noon on Tuesday by 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;learned about the case;-;All;the robbers appeared to be men, although they may have been attempting to;disguise their appearances.;-;There;were either 3 or 4 robbers - we?re not sure due to conflicting eye-witness;accounts;-;The;getaway car was a late-model 4-door sedan that was a dark 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, Patty will be told all the;known information by the police investigators who responded to the emergency;call at 12:05pm on Tuesday. This will consist of the separate eye-witness;accounts the police investigators collected as well as police conjectures.;She likes to record her notes using;simple logic statements. Use the;following 4 statements to express the given compound statement given by each;eye-witness and the police investigators;p: There were 4 bank robbers;q: All the bank;robbers were men;r: One robber;had a ponytail;s: The getaway;car was blue;You may use AND, OR, NOT, XOR, and;ARROW instead of the logic symbols used in the notes, but be sure to use;parenthases as needed to represent precedence.;p AND q ARROW r is not the same thing as;p AND (q ARROW r).;a. One robber had a ponytail or all the bank;robbers were men, but there were only 3 bank robbers;Answer;Explanation;b. There were 4;bank robbers, but all the bank robbers;were men and one robber had a ponytail;Answer;Explanation;c. If there;were 4 bank robbers and one of the robbers had a ponytail, then all the bank;robbers were men;Answer;Evaluation;d. If the;getaway car was blue then one robber had a ponytail and there were not 4 bank;robbers;Answer;Explanation;e. Either the;getaway car was blue or one robber had a ponytail (but not botH), and all the;bank rubbers were men.;Answer;Explanation;Task #2: (5 points);The writers can?t decide who the leader of the bank robbers should;be. They think that the leader should;either be a female (disguised as a man) or someone with black hair (but not;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 the combinations of;these three characteristics (gender, hair color, short/tall). Given these 3 simple statements, determine;the correct compound statement for the condition stated above, then determine a;truth table for that statement.;p: The leader;is a female;q: The leader;has black hair;r: The leader;is tall (over 5? 10?);p;q;r;T;T;T;T;T;F;T;F;T;T;F;F;F;T;T;F;T;F;F;F;T;F;F;F;Task #3;(10 points) The writers and actors have finally agreed on the;characteristics for the leader of the bank robbers. Based on the results of focus groups and;extensive research, they have tried all the following combinations for the;following three statements;p: The leader;has black hair;q: The leader;is female;r: The leader;is tall (over 5? 10?);The focus groups seemed to zoom in on;one particular combination, as shown in this truth table;p;q;r;T;T;T;F;T;T;F;F;T;F;T;F;T;F;F;T;F;T;T;F;F;T;F;F;F;F;T;F;F;F;F;F;You are given the descriptions for the six;actors/actresses under consideration.;Actor A;-;male;-;6?;tall;-;bald;Actress B;-;female;-;5?;5?;-;black;hair;Actor C;-;male;-;5?;5?;-;black;hair;Actor D;-;male;-;5?5?;-;red;hair;Actor E;-;male;-;6?;-;black;hair;Actor F;-;male;-;5?6?;-;bald;Using the evidence from above and what you have learned about logic, explain in;a well-structured essay which person should play the part of the leader of the;bank robbers. Your answer should;include 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;then evaluate 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 your position

 

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