Every human being is an animal.
No tree is a human being.
Therefore, there are no trees that are animals.
Answer questions ‘a’ to ‘j’ below from the passage immediately above.
a)If the statement “no trees are animals” is true, what is the immediate inference of this
‘E’
statement?
No animals are trees.
b)What is the obverse of the A - statement above?’
All trees are non-animals.
c)What is the converse of the statement, ‘no trees are human beings?’
No human beings are trees.
d)Is the converse of the statement in ‘C’ above true?
Yes
e)Rewrite the argument above as a standard-form categorical syllogism
All human being are animals
No trees are human beings.
So, no trees are animals.
f)Identify its mood and figure:
The mood of this argument is AEE and it contains a second figure.
g)
Test its validity using a Venn diagram
h)What can be said about the validity of the argument above?
After the premises have been diagrammed the argument has been deemed invalid the
relationship between ‘T’ and ‘A’ was not declared empty and as such the premises did not
guarantee the conclusion.
i)Why would or would you not use a truth table to test the argument above?
I would not use a truth table to test this argument considering that truth tables are used for
larger class arguments that contain compound statements.
j)Why would or would you not use an argument diagram to test this argument?
I wouldn’t use an argument diagram because with the structure of this argument it would
not be necessary to break it down into parts and figure out how related they are.
k)Use your own substitution instances to demonstrate how contraries work.
‘All doctors have knowledge of bodily functions’ is true then it’s contrary would be ‘No doctors
have knowledge of bodily functions’ which is false because as the rule states, both cannot be true
but both can be false.
l)Use some substitution instances to show how sub-contraries work.
‘Some bananas on the table are ripe’ and ‘Some bananas on the table are not ripe’ are
subcontraries because it is possible for us to walk into a room and see either ripe or green
bananas sitting on the table.
m)Use Venn diagrams to prove that the converse of ‘I’ statements is always true.

‘Some children are toddlers.’ The converse of this ‘I’ statement would be ‘Some toddlers
are children.’

‘Some Asians are Thai.’ converses to ‘Some Thai are Asians.’
2) While [colleges and universities have come under heavy criticism in the last decade,] [they
will undoubtedly remain a vital force in American social life for generations to come.] For one
thing, although [both the public and the media seem to have a thirst for stories about people
who’ve gotten rich or famous with only a high school degree,] the fact remains that [a college or
university degree is the surest way to increase one’s social and occupational status.] For another,
[college grads as a group indicate higher levels of satisfaction with their lives than do those with
1
2
3
4
5
lesser educational attainments.] Finally, [you show me a nation with a weak system of higher
education and I’ll show you a nation with little power.] And [Americans will never willingly
accept a position of relative powerlessness among the nations of the world.]
6
7
Answer questions ‘a’ to ‘h’ below from the passage immediately above.
a)
Give two (2) reasons as to how you know that the above passage is an argument.

This passage is an argument because it contains premises and a conclusion.
b) Identify from the above passage and explain any two (2) violations of well-crafted arguments.
Excess verbiage is found in premises 3 and 4 namely the examples of discount and assurance
and also the confusion of sub conclusions with final conclusions. Excess verbiage are words
or statements that add nothing to the argument and confusing the sub conclusion with the
final conclusions happens when the author argues in steps by the first claim, the sub
conclusion and then uses it to argue for the final conclusion.
c) In composing a well-crafted version of the above argument, how is each of the violations
identified above dealt with?
For not confusing the sub conclusion with the main conclusion the argument is
restructured and we place and for excess verbiage we remove the discount and assurances.
d)
Construct an argument diagram to show the links between the statements.
5
6+7
4
2
e)
What is the relationship between statements 6 and 7 on the argument diagram?
The relationship between 6 and 7 is that both premises are interdependent and in
conjunction with the other.
f) Is this argument an example of an inductive or a deductive argument?
This argument is an example of an inductive argument.
g)
How can you tell whether this argument is valid, invalid weak or strong?
The argument is strong because the premises provided probable true support to the conclusion. An
argument with a strong point is one that shows that if the premises are true then the conclusion is
true.
h) Of all the methods of testing arguments that were employed in this module between units 1 to 7, which
one is the most appropriate for testing the above argument?
A truth table would be the most appropriate method of testing this argument.
i) Construct an argument that is an example of an enthymeme.
Mary is a mathematics teacher. So Mary knows all the mathematical formulas.
j) Explain exactly what makes your example in ‘i’ above an enthymeme.
This is an enthymeme because one of the premises has not been stated.
k)
Provide two (2) examples of formal fallacies.
All tigers are carnivores. All lions are carnivores. All tigers are lions.
If it is sunny, then I will wear a hat. I am wearing a hat. So, it is sunny.
l)
Explain what makes these forms fallacious.
These forms are fallacious because they have errors in the structure of the argument.
m) Test these forms to confirm that they are fallacious and misleading.
To test these forms we will use the Mill’s Method of concomitant variation
.
n) Determine the validity of the form ‘If A then B. Not B. So, A’ by using a truth table. Explain your
results.
A → B, ~ B, ∴ A
A
B A→B ~B ∴A
T
T
F
F
T
F
T
F
T
F
T
T
F
T
F
T
T
T
F
F
From the truth table presented above the form ‘If A then B. Not B. So, A ’ is valid as it shows the
conclusion is false only when both premises are true or in this instance when both ‘A’ and ‘B’
values are false.
o) Construct a counterexample to test the validity of the form in ‘n’ above.
If Usain Bolt is a bird, then he has wings. Usain Bolt does not have wings. So, Usain Bolt is a bird.
p) Interpret your results for ‘o’ above.
The results from the counterexample above prove that the validity is invalid. ..