Name:________________________________________
Phi 120 – Exam 1
General Instructions: Please print out this exam and write in your answers and turn the test in at the
start of class on Wednesday March 5. Answers need to be legible (If I can’t read your writing, I will not
grade the question). I suggest using a pencil so as to be able to erase answers which you may need to
change. You may use the book, class notes and smart-board notes. Please do not use tutors or online
help or other classmates (note: some of the definitions I give are slightly different than definitions found
elsewhere, hence online surfing for answers will usually not help anyway)
If you need clarification about any question, please email me for further guidance.
No late tests will be accepted. If you are going to miss class, then you may place it in my inbox by going
to CC223 (The adjunct faculty office) and giving it to the receptionist there to place in my mail box. Email
me if you do this, so I will know to pick it up.
Part 1. Entailment, Relevance and Independence.
Write E if p entails q, write R if p is relevant to q, and write I if p is independent of q (2 points each)
p = “Today is Monday and tomorrow is John’s birthday”
q = “Tomorrow is John’s birthday”
p = “The book has over 500 pages”
q = “The book weighs more than 3 ounces”
p = “If the economy grows, then student enrollment will increase, but student enrollment has
not increased”
q = “The economy has not grown”
p = “Water is necessary for human life”
q = “The Cullian diamond is over 3106 carats in weight”
p = “Janet’s mother is named Violet”
q = “Janet’s daughter is named Violet”
Part 2. The relations of entailment, independence and relevance are all mutually exclusive (this means a
pair of statements can not be considered as examples of two or more of these terms at the same time,
for example if p entails q, then p is not independent of q and p is not relevant to q. However, I
mentioned in class that other relationships between statements exist. In this exercise, we will
“discover” another such relationship. (5 points each)
Let p be, “Today is Monday” and let q be “Today is Wednesday”.
Does p entail q? Why or why not?
Is p relevant to q? Why or why not? (here answer “no” if the truth of p tells you something certain about
the truth of q)
Is p independent of q? Why or why not?
If p is true, what truth value must q have?
If q is true, what truth value must p have?
Is it possible for both p and q to be false? Explain?
Using the above information, we will define a new relation between statements, called contraries.
Definition: Two (or more) statements are contraries if . . . (fill in the rest of the definition based on the
information you learned above – the last three questions give you all the needed information).
Part 3. CREATE an example of an argument (please create one, do NOT use something you find on the
internet or something that is written in our textbook or any other textbook). Number each sentence (or
phrase) as appropriate. After writing down your argument, indicate whether each numbered sentence
is a premise or the conclusion. (10 points)
Now analyze your argument. Using the concepts of valid, invalid, sound, unsound, cogent, uncogent,
strong and weak, indicate which of the above apply to your argument, and why (use every term which
applies – there will be at least two) (5 points)
Part 4. Answer true or false, and provide a brief justification for each. Acceptable justifications
appeal to definitions and/or use illustrative examples -usually in the case where the answer is
false. (2 points each)
_________
Arguments with valid inferences always have a true conclusion.
_________
Arguments must have at least one conclusion, and at least one premise.
_________
If the conjunction of the premises of an argument are relevant to the
conclusion, then the argument’s inference is invalid.
_________
If all of the premises of an argument are contraries, then the argument’s
inference is valid.
_________
An unsound argument must have all false premises, while having an inference
which is valid.
Part 5. Classify the following arguments as valid, invalid, sound, unsound, strong, weak, cogent,
uncogent. Write down all which apply, no need to provide justification. (5 points each)
Every horse which has been known to man was born without wings and unable to fly. Hence
when our mare has a foal, it will be born without wings and unable to fly.
If rain falls from clouds, then everyone wins the lottery.
Everyone does not win the lottery.
Therefore rain does not fall from clouds.
The door was left open or the window was left unlocked.
The door was left open
Therefore the window was not left unlocked.
(Assume all premises are actually true)
John owns a large hat. People who own large hats have large heads. People with large heads are
very smart. Hence John is very smart.
Mary’s husband won the lottery last week. The odds were over 1 in a million. Since Mary’s
husband works at the same place as my husband, and our families have so much in common,
then we will win the lottery too.
Only 1 in 10,000 people get this rare form of disease. The disease itself is known not to be
inherited or the result of any action or behavior on the part of those who get the disease. All
evidence indicates that the disease strikes at random. Hence such conditions make it unlikely
that I will get the disease. (assume the premises are true)
Part 6. Write down the form of the following arguments, and use that information to determine
whether the argument’s inference is valid or invalid, (make sure you write down whether it is
valid or invalid). (5 points each)
If milk costs more than 4 dollars a gallon, then I will stop drinking so much milk.
Milk does cost more than 4 dollars a gallon.
Therefore I will stop drinking so much milk.
The bookstore will have the book, or I will order it online.
The bookstore does not have the book.
Therefore I will order it online.
If Sandra needs glasses, we will have to go to the Optometrist next week.
We don’t have to go to the Optometrist next week.
Hence Sandra does not need glasses.
If the diplomats are expelled, then the U.S. will require stricter VISA requirements.
The diplomats were not expelled.
Therefore the U.S. will not require stricter VISA requirements.
If I take more than 6 credits, then I will have to get another job.
I had to get another job.
Therefore I took more than 6 credits.
Part 7. Use the criteria listed below from our handout on argument analogies
(http://www.oakton.edu/user/4/ebottorf/Lecture20.pdf) to analyze the strength or weakness
of the argument which follows.
1.  Relevant similarities.
2.  Relevant dissimilarities.
3.  The number of instances compared.
4.  Diversity among cases.
Certain cultures have a lower incidence of heart disease than other cultures. Japan is
one culture which has a much lower incidence of heart disease than the same
comparative population in the United States. Since the Japanese eat more fish and seafood than the average U.S. citizen, if U.S. citizens changed their diets to include more
fish and sea-food, they would, in general, lower their chance of getting heart disease.
BONUS ( 10 points, optional)
Consider the following argument:
Today is July 4.
July 4th is independence day, which falls on Tuesday this year.
Independence day is always sunny here.
Sunny days always get up to at least 65 degrees.
But today the temperature only got up to 59 degrees all day long.
Hence, next year fire-works will be half-price.
Classify the argument according to the normal classification scheme (valid, invalid, sound,
unsound, weak, strong, cogent, uncogent). Justify your answer.
Note – this is graded as all-or-nothing, no partial credit for bonus questions is given.