MM250 Unit 2 Assignment 48849

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 the symbol 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:

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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:
q:
r:

NE region had higher monthly sales than the SW region
NE region had higher monthly sales than the SE region
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:

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4.

(2 points) Complete the following truth table for the logical statement [(~p ? q) ? ?r]
p
T
T
T
T
F
F
F
F

q
T
T
F
F
T
T
F
F

r
T
F
T
F
T
F
T
F

~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 table
p
T
T
T
T
F
F
F
F

q
T
T
F
F
T
T
F
F

r
T
F
T
F
T
F
T
F

~q

(p ? r)

(r ? ~q)

( 1 point) Conclusion: These statements are (pick one)
EQUIVALENT

(p ? r) ? ~q

p ? (r ? ~q)

EQUIVALENT

NOT

Answer:

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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:

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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:
q:
r:

The leader is a female
The leader has black hair
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

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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:
q:
r:

The leader has black hair
The leader is female
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

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

T

Unfortunately, this
part was obscured
by a water stain.

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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