APPROVED
EXAMINATION PAPER:
ACADEMIC SESSION 2008/2009
CAMPUS
Maritime Greenwich
SCHOOL
Humanities and Social Sciences
DEPARTMENT
History, Philosophy and Politics
LEVEL
ONE
COURSE TITLE
HOW TO ARGUE: CRITICAL REASONING, LOGIC
AND RHETORIC
COURSE CODE
PHIL1051
DURATION
(including reading time)
2 Hours
DATE AND TIME
May 2009
INSTRUCTIONS TO CANDIDATES AND INVIGILATORS
Read carefully and try to answer all of the questions in the spaces provided.
If you run out of space, use the extra sheets at the end of the question paper to
complete your answer.
1
How to Argue logic examination 2008-09
1. Answer the following questions as precisely as you can.
a. When is an argument invalid?
2
b. Under what circumstances is an argument judged to be sound?
2
c. What methods can be used in order to prove that an argument is valid?
2
2. Each of the sentences below gives expression to one of the following logical
operators: AND, OR, IF…THEN. Identify which operator is being used in each case.
a.
The man was either a fool or a liar
b.
Although the book was long, there was little substance to its claims.
c.
If it continues to rain, I shall be soaked.
d.
You will be allowed to sit the test provided you have attended classes.
e.
I will finish this book unless the library recalls it.
2
2
2
2
2
3. Identify the simple statements (making adjustments to syntax as necessary). Assign
them letters and then and write them down in symbolic form using the appropriate
logical operator. The first one has been done for you.
The people will die unless they are fed
a. Although it was warm, she wore a jumper.
The people will die = P
The people will be fed = Q
PvQ
2
2
b. The book was short but tedious
2
c. If you eat loads of cream cakes, you’ll get fat
2
d. They will surely die of cold unless they come in
soon.
2
4. Put into symbolic form the following arguments, using the symbols P, Q and R. State
whether the arguments are valid or invalid and, where appropriate, name the rule of
inference being used. The first argument has been done for you.
argument
Eating meat is unhealthy if meat contains
a lot of cholesterol. Meat does contain a lot
of cholesterol. Therefore, eating meat is
unhealthy.
a. Either the animals used in research are
a lot like humans, or they are not a lot like
humans. If the animals are a lot like
humans, then experimenting on them is
morally questionable. If the animals are
not a lot like humans, then experimenting
on them is pointless. So, either
experimenting on animals is morally
questionable, or it is pointless.
form
QP
Q
P
Valid/Invalid
valid
rule
Modus ponens
4
b. Sam is wealthy if he has a million
pounds. But Sam does not have more than
a million pounds. Therefore, Sam is not
wealthy.
4
3
c. If it is raining, then the ground is wet.
The ground is not wet. Therefore, it is not
raining.
4
d. Either Bach wrote Prometheus or
Scriabin wrote it. Bach did not write it.
Therefore, Scriabin wrote Prometheus
4
e. If God cannot prevent suffering, then
God is not omnipotent. If God does not
want to prevent suffering, then God is not
perfectly good. But either God cannot
prevent suffering or God does not want to
prevent suffering. So, either God is not
omnipotent or God is not perfectly good.
4
5. Demonstrate that the law of non-contradiction by means of a truth table.
2
6. Explain how the truth table proves this law is a tautology.
2
4
7. Determine the truth values of the following complex statements making the following
assumptions about the truth value of the simples statements:
A is True
B is True
C is False
D is False
statement
a.
Truth value
1
A&D
b.
2
– (C v D)
c.
2
- (D v C) → B
8. What truth values must be assigned to the simple statements P and Q, in order to
make the following compounds FALSE? The first has been done for you.
Ensure that you have shown your truth tables in your answer.
compound
simples
- (P ↔ Q ) → Q
→Q)→Q
P
Q
- (P
T
T
F
T
T T
T
F
T
F
F F
F
T
F
T
T T
F
F
F
T
T F
a.
Situation 2 where
P = True
Q = False
2
– (P & Q)
5
b.
2
– P v (P & Q)
c.
2
– (P v Q) → – ( P & ( Q v P ))
9. Construct truth tables to determine whether the following arguments are valid or
invalid. Note that the premises are separated by commas. Indicate how the truth table
supports your answer. Your answers must include truth tables.
a.
– P, P v Q,  Q
2
6
b.
c.
– Q, P → Q,  – P
– Q, (P & Q) → R, – (R & Q),
3
R
3
7
10. Formalise the following argument and then construct a truth table to evaluate
whether it is valid or invalid. Indicate how the truth table supports your answer.
If Socrates works hard, he gets rich. But if Socrates doesn’t work hard, he enjoys life.
Moreover, if Socrates does not get rich, then he does not enjoy life. Hence Socrates gets
rich.
H = Socrates works hard. R = Socrates gets rich. L = Socrates enjoys life.
3
11. The following argument proceeds by logical steps to prove a valid conclusion.
Indicate from which steps the inferences on lines 5, 6 and 7 are drawn and by which rule
the inference is made.
Problem
Solution
3
1. H v –C
2. H  -B
3. –C  D
4. (-B v D)  (K & J)
----------------------------------------------------------------------------5. –B v D
6. K & J
7.  J
8
12. Symbolise the following argument using the scheme of abbreviation given. Use the
technique of logical deduction using rules of inference to demonstrate how the
conclusion can be logically arrived at from the premises.
Dinosaurs are extinct. Given that dinosaurs are extinct, they suffered from some catastrophe 6
if they died suddenly. The dinosaurs died suddenly, assuring that they froze due to a sudden
drop in temperature or they were attacked by a lethal virus. The dinosaurs froze due to a
sudden drop in temperature provided that the sun’s rays were blocked. The earth’s
atmosphere was filled with dust due to the impact of a comet, and the sun’s rays were
blocked. Therefore the dinosaurs suffered some catastrophe.
E: Dinosaurs are extinct. C: the dinosaurs suffered from some catastrophe.
D: the dinosaurs died suddenly. F: the dinosaurs froze due to a sudden drop in temperature.
V: the dinosaurs were attacked by a lethal virus. S: the sun’s rays were blocked.
A: the earth’s atmosphere was filled with dust due to the impact of a comet.
13. Assess the following arguments for validity using venn diagrams.
1. All women are
people. All people are
finite beings. Therefore
no finite being is a
woman.
3
9
2. All egalitarians
believe that men are
equal. No people who
believe that men are
equal are anti-human
rights. Therefore some
egalitarians are not
against human rights.
3
3. No fish are cats, but
some collie dogs are
not cats. So, some
collie dogs are fish.
3
4. All idealists struggle
with material
substance. Some
positivists do not
struggle with material
substance. Thus some
positivists are not
idealists.
3
10
14. Give the symbolic form of these ordinary language arguments and then generate a
counterexample to show that the form is invalid. Use the symbols A, B and c. The first
argument has been completed for you. Note that you get marks for both parts of this
exercise.
argument
All people who despise
animals are neurotic. No
veterinarian is a person who
despises animals. Hence no
veterinarian is a neurotic.
form
All A are B
No C is an A
So, No C is a B
Substitution instance
All spaniels are dogs
No greyhound is a spaniel
So, no greyhounds are dogs
a. All miracles are highly
improbable events. Some
highly improbable events
are cases of winning the
lottery. So, some cases of
winning the lottery are
miracles.
2
b. No rock is sentient. Some
mammals are sentient.
Hence, no mammal is a
rock.
2
15. Symbolise the following statements using the schemas and abbreviations provided.
Every logic student is wise.
(Lx: x is a logic student; Wx: x is wise)
1
Everything is an illusion.
(Ix: x is an illusion)
2
If anyone is sad, then he or she is not happy.
(Sx: x is sad; Px: x is a person; Hx: x is happy)
2
11
Rough workings
12
Rough workings
13