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kaplan MM250 Unit 2 assignment

Question # 00013919
Subject: Mathematics
Due on: 05/12/2014
Posted On: 04/30/2014 02:57 AM

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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.

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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)Ú~r]

p

q

r

~r

~p

~p? q

[(~p? q)Ú~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, (pÚ r)? ~q with pÚ (r?~q), using the following truth table.

(2 points) Complete the following truth table

p

q

r

~q

(pÚ r)

(rÚ ~q)

(pÚ r)? ~q

pÚ (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

.jpg">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

.gif" alt="Rectangular callout: unfortunately, this part was obscured by a water stain.">.jpg">

T

T

T

F

T

T

F

F

.gif">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

Tags aignment unit mm250 kaplan explanation table points truth answer robbers statement following bank region house hair statements temperature black using actor police logic male leader investigators ponytail given robber aignment

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Preview: Answer xxxxxxxxxx Part xx Case Study xxx case of xxx Noon-time xxxxxxx xxxx week xxxxx Madeye will xx investigating a xxxx robbery xxx xxxx Street xxxx was robbed xx exactly 12 xxxx on xxxxxxx xx either x or 4 xxx The group xxxxxxx in x xxxxxxx car, xxxxx has not xxxx recovered From xxx police xxxxxxxxxxxxx xxxxx what xx will have xxxxxxx about the xxxx All xxx xxxxxxx appeared xx be men, xxxxxxxx they may xxxx been xxxxxxxxxx xx disguise xxxxx appearances There xxxx either 3 xx 4 xxxxxxx x were xxx sure due xx conflicting eye-witness xxxxxxxx The xxxxxxx xxx was x late-model 4-door xxxxx that was x dark xxxxx xxxxxxx blue, xxxxx or dark xxxxxx Task 1 xx points x xxxxx each) xx the first xxxxx of the xxxxx Madeye xxxxxxxxx xxxx week, xxxxx will be xxxx all the xxxxx information xx xxx police xxxxxxxxxxxxx who responded xx the emergency xxxx at xxxxxx xx Tuesday xxxx will consist xx the separate xxxxxxxxxxx accounts xxx xxxxxx investigators xxxxxxxxx as well xx police conjectures xxx likes xx xxxxxx her xxxxx using simple xxxxx statements Use xxx following x xxxxxxxxxx to xxxxxxx the given xxxxxxxx statement given xx each xxxxxxxxxxx xxx the xxxxxx investigators p xxxxx were 4 xxxx robbers x xxx the xxxx robbers were xxx r One xxxxxx had x xxxxxxxx s xxx getaway car xxx blue You xxx use xxxx xxx NOT, xxxx and ARROW xxxxxxx of the xxxxx symbols xxxx xx the xxxxxx but be xxxx to use xxxxxxxxxxx as xxxxxx xx represent xxxxxxxxxx p AND x ARROW r xx not xxx xxxx thing xx p AND xx ARROW r) x One xxxxxx xxx a xxxxxxxx or all xxx bank robbers xxxx men, xxx xxxxx were xxxx 3 bank xxxxxxx Answer (r x q) x x Explanation xxxxx part of xxx statement is xxxx or xxxxxxx xxx statements xxxxxxx above i x r and x.....
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