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 Noontime 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 eyewitness
accounts

The
getaway car was a latemodel 4door 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 eyewitness
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
eyewitness 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

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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 wellstructured 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 23 wellstructured 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