1. The following text material and terms defined at the end
comprise part of what will be asked on the Mid-Term Exam for
PHIL 1381.
Logic [excerpt from Stan Baronett, Logic, 2E]
Logic is the study of reasoning. Logic investigates the level of
correctness of the reasoning found in arguments. An argument is
a group of statements of which one (the conclusion) is claimed
to follow from the others (the premises). A statement is a
sentence that is either true or false. Every statement is either
true or false; these two possibilities are called “truth values.”
Premises are statements that contain information intended to
provide support or reasons to believe a conclusion. The
conclusion is the statement that is claimed to follow from the
premises. In order to help recognize arguments, we rely on
premise indicator words and phrases, and conclusion indicator
words and phrases.
Inference is the term used by logicians to refer to the reasoning
process that is expressed by an argument. If a passage expresses
a reasoning process—that the conclusion follows from the
premises—then we say that it makes an inferential claim. If a
passage does not express a reasoning process (explicit or
implicit), then it does not make an inferential claim (it is a
noninferential passage). One type of noninferential passage is
the explanation. An explanation provides reasons for why or
how an event occurred. By themselves, explanations are not
arguments; however, they can form part of an argument.
There are two types of argument: deductive and inductive. A
deductive argument is one in which it is claimed that the
conclusion follows necessarily from the premises. In other
words, it is claimed that under the assumption that the premises

2. are true it is impossible for the conclusion to be false. An
inductive argument is one in which it is claimed that the
premises make the conclusion probable. In other words, it is
claimed that, under the assumption that the premises are true, it
is improbable for the conclusion to be false.
Revealing the logical form of a deductive argument helps with
logical analysis and evaluation. When we evaluate deductive
arguments, we use the following concepts: valid, invalid, sound,
and unsound. A valid argument is one where, assuming the
premises are true, it is impossible for the conclusion to be false.
In other words, the conclusion follows necessarily from the
premises. An invalid argument is one where, assuming the
premises are true, it is possible for the conclusion to be false. In
other words, a deductive argument in which the conclusion does
not follow necessarily from the premises is an invalid argument.
When logical analysis shows that a deductive argument is valid,
and when truth value analysis of the premises shows that they
are all true, then the argument is sound. If a deductive argument
is invalid, or if at least one of the premises is false (truth value
analysis), then the argument is unsound.
A counterexample to astatement is evidence that shows the
statement is false, and it concerns truth value analysis. A
counterexample to an argument shows the possibility that
premises assumed to be true do not make the conclusion
necessarily true. A single counterexample to a deductive
argument is enough to show that an argument is invalid.
When we evaluate inductive arguments, we use the following
concepts: strong, weak, cogent, and uncogent. A strong
inductive argument is one such that if the premises are assumed
to be true, then the conclusion is probably true. In other words,
if the premises are assumed to be true, then it is improbable that
the conclusion is false. A weak inductive argument is one such
that if the premises are assumed to be true, then the conclusion

3. is not probably true. An inductive argument is cogent when the
argument is strong and the premises are true. An inductive
argument is uncogent if either or both of the following
conditions hold: the argument is weak, or the argument has at
least one false premise.
What Logic Studies
Logic is the study of reasoning. Its aim is to distinguish correct
from incorrect reasoning by establishing the rules or patterns of
successful arguments. Typically, we begin a study of logic with
a discussion of certain features of language essential to
arguments.
A. Statements and Arguments
A statement is a sentence that is either true or false, that is, a
statement has a truth value. Statements are the primary building
blocks of an argument. An argument is a collection of two or
more statements, one of which is supported by the other or
others. The conclusion is the supported sentence, while the
premises are the sentences that support the conclusion.
The goal of every argument is to establish the conclusion on the
basis of the evidence provided by the premise or premises. Thus
what distinguishes an argument from other collections of
statements is its inferential nature. An argument’s elements
reflect a conceptual flow from premises to conclusion. So,
“inference” means the reasoning process expressed by an
argument.
“Statement” is distinguished from “sentence” and “proposition”
as follows:
1. A sentence is a set of words complete in itself, as in a
statement, question, or exclamation.

4. 2. A statement is a sentence that has two possible truth values:
true and false.
3. A proposition is the information content or meaning of a
statement.
B. Recognizing Arguments
An argument is distinguished from other collections of
statements by its inferential nature. Unlike other passages, an
argument involves drawing an inference from one or more
statements to another statement. We say that a passage makes an
inferential claim when it expresses a reasoning process, i.e.,
that the conclusion follows from the premises.
Drawing an inference is a purely intellectual act. For example,
you don’t know what a dibbeltot is, nor do you know what
fizzlestrums and poggurets are. Nevertheless, you can draw an
inference from the following statements:
No dibbeltot is a fizzlestrum. Every fizzlestrum is a pogguret.
The inference you draw is “No dibbeltot is a pogguret.”
One way to identify the elements of an argument is through
indicator words. Conclusion indicators alert you to the
appearance of a conclusion, while premise indicators alert you
to the appearance of a premise. In each case, indicator words
tell you that a conclusion or premise is about to be asserted or
has just been asserted.
C. Arguments and Explanations

5. Distinguishing between arguments and non-arguments can
sometimes be tricky. This is especially the case with
explanations. Depending on the context, an explanation can be
taken for an argument and vice versa. In addition, both
arguments and explanations often use the same indicator words.
The crucial distinguishing feature of an argument is that the
conclusion is at issue. So, even when an explanation involves
indicator words, if there is nothing at issue, the passage does
not become an argument: “Because you were late meeting me at
the restaurant for dinner, I went ahead and placed my order.”
Here, an explanation is offered for ordering food. There is no
intent to prove anything or settle some sort of issue.
D. Truth and Logic
Because an argument involves an inferential claim, we say that
the truth of the conclusion depends on how good a job the
premises do in establishing that truth. In this way, logic is
concerned with truth in a rather different way than we
determine the truth or falsity of a given statement. Logical
analysis involves bearing in mind this distinction. Take another
look at the example in B above:
No dibbeltot is a fizzlestrum.
Every fizzlestrum is a pogguret.
Therefore, no dibbeltot is a pogguret.
Consider another type of example:
Whenever I come home, my dog is so happy to see me that he
jumps all over me. So, when I get home later today, my dog will
be so happy to see me that he’ll jump all over me.
Whether or not each of the statements is true is irrelevant to the

6. question of whether or not the premises do a good job of
establishing the conclusion.
E. Deductive and Inductive Arguments
Arguments fall into one of two types: those that rely on
experience and those that do not. Each of the two arguments we
just saw in D above is an example of, respectively, deductive
and inductive argumentation. We do not need experience—what
we smell, taste, see, etc.—in order to reason to the conclusion,
“No dibbeltot is a pogguret.” In fact, we have no experience of
these things. Nevertheless, we can reason successfully to the
conclusion by the way the premises’ elements relate to each
other. The dog argument is different in that the conclusion is a
prediction which relies on past experience.
A deductive argument is one in which the conclusion is claimed
to follow necessarily from the premises. In other words, the
premises are claimed to guarantee the conclusion, or it is
impossible for the conclusion to be false if the premises are
true.
An inductive argument is one in which the conclusion is
claimed to follow with a degree of probability. In other words,
the premises make it likely for the conclusion to be true, or it is
improbable that the conclusion is false if the premises are true.
F. Deductive Arguments: Validity and Truth
Deductive arguments are either valid or invalid, and sound or
unsound. A valid deductive argument is one in which it is
impossible for the conclusion to be false, if the premises are
true. An invalid argument is one in which it is possible for the
conclusion to be false, if the premises are true.
A sound argument is valid, and its premises are actually true.

7. All invalid arguments are, by definition, unsound.
Valid + True Premises = Sound
Valid + At Least One False Premise = Unsound
Invalid = Unsound
A convenient test of validity is the counterexample method. If
you can find a counterexample to an argument’s conclusion
(while the premises are true), you have shown the conclusion is
false. When you extend this method to an argument, you
demonstrate the argument is invalid. First, however, be sure that
your counterexample matches the original argument’s form.
G. Inductive Arguments: Strength and Truth
Inductive arguments are evaluated first according to how strong
or weak the relation is between the premises and the conclusion.
An inductive argument is strong when, assuming the premises
are true, it is improbable for the conclusion to be false. An
inductive argument is weak when, assuming the premises are
true, it is probable for the conclusion to be false.
A further evaluation involves the actual truth of the premises. A
strong argument is cogent when the premises are true. A strong
argument is uncogent when at least one of the premises is false.
All weak arguments are uncogent, since strength is a part of the
definition of cogency.
Strong + True Premises = Cogent
Strong + At Least One False Premise = Uncogent
Weak = Uncogent

8. Deductive and Inductive Arguments
The basic difference between deductive and inductive
arguments is experience. When you reason deductively, you
reason without relying on experience—without relying on what
your five senses tell you. When you reason inductively, you
reason according to experience.
Here’s an example of reasoning deductively: “All the dibdabs
are skeezics. All the skeezics are runnels. Therefore, all the
dibdabs are runnels.” You don’t have experience with dibdabs,
skeezics, or runnels because they’re made up! You can’t see,
taste, smell, touch, or hear them. The way that you are certain
the conclusion is true, namely that all the dibdabs are runnels is
because your intellect has processed the relations between the
groups of things.
Here’s an example of reasoning inductively: “My car won’t
start. In fact, when I put the key in the ignition, the car won’t
turn over. It’s silent. Therefore, my battery is dead.” How can
you be so confident that your battery is dead? Aren’t there other
potential causes of the car not starting? Yes, but given your
previous experience—or similar experiences you’ve heard
about—it seems most likely to you that the most likely reason
your car won’t start is that there’s a problem with the battery.
Notice that, in this case, you reasoned by way of experience.
Deductive Arguments: Validity and Truth
Valid Argument: When an argument is valid, it’s impossible
to make the conclusion false, if the premises are true. Another
way to think about validity is in terms of what happens when
you accept the premises of a valid argument but deny the
conclusion. In that case the denial contradicts what you’ve
accepted as true. If I say, “I have candy in my left hand or my

9. right hand,” and then I open up my left hand to reveal there’s
nothing in it, you’d conclude that the candy is in my right hand.
But, suppose I say instead, “I don’t have candy in my right
hand.” You’d say, “That’s impossible! You just said you have
candy in either your left hand or your right hand but when you
opened your left hand, there was no candy. If it’s true to say, ‘I
have candy in my left hand or my right hand, but I do not have
candy in my left hand,’ you can’t logically deny you have candy
in your right hand. It doesn’t make sense to do that!” When we
accept the premises of a valid argument, we are committed to
the truth of the conclusion.
Important words used in logical analysis
Argument: A group of statements of which one (the conclusion)
is claimed to follow from the others (the premises).
Statement: A sentence that is either true or false.
Premise: The information intended to provide support for a
conclusion.
Conclusion: The statement that is claimed to follow from the
premises of an argument.
Logic: The study of reasoning.
Truth value: Every statement is either true or false; these two
possibilities are called “truth values.”
Proposition: The information content imparted by a statement,
or simply put, its meaning.
Inference: A term used by logicians to refer to the reasoning
process that is expressed by an argument.
Conclusion indicators: Words and phrases that indicate that the
presence of a conclusion (the statement claimed to follow from

10. premises).
Premise indicators: Words and phrases that help us recognize
arguments by indicating the presence of premises (statements
being offered in support of a conclusion).
Inferential claim: If a passage expresses a reasoning process—
that the conclusion follows from the premises—then we say that
it makes an inferential claim.
Explanation: An explanation provides reasons for why or how
an event occurred. By themselves, explanations are not
arguments; however, they can form part of an argument.
Deductive argument: An argument in which it is claimed that
the conclusion follows necessarily from the premises. In other
words, it is claimed that under the assumption that the premises
are true it is impossible for the conclusion to be false.
Inductive argument: An argument in which it is claimed that the
premises make the conclusion probable. In other words, it is
claimed that under the assumption that the premises are true it
is improbable for the conclusion to be false.
Valid deductive argument: An argument in which, assuming the
premises are true, it is impossible for the conclusion to be false.
In other words, the conclusion follows necessarily from the
premises.
Invalid deductive argument: An argument in which, assuming
the premises are true, it is possible for the conclusion to be
false. In other words, the conclusion does not follow necessarily
from the premises.
Sound argument: When logical analysis shows that a deductive
argument is valid, and when truth value analysis of the premises

11. shows that they are all true, then the argument is sound.
Unsound argument: If a deductive argument is invalid, or if at
least one of the premises is false (truth value analysis), then the
argument is unsound.
Counter-example: A counterexample to a statement is evidence
that shows the statement is false. A counterexample to an
argument shows the possibility that premises assumed to be true
do not make the conclusion necessarily true. A single
counterexample to a deductive argument is enough to show that
the argument is invalid.
Strong inductive argument: An argument such that if the
premises are assumed to be true, then the conclusion is probably
true. In other words, if the premises are assumed to be true, then
it is improbable that the conclusion is false.
Weak inductive argument: An argument such that if the
premises are assumed to be true, then the conclusion is not
probably true.
Cogent argument: Strong and the premises are true.
Uncogent argument: An inductive argument is uncogent if
either or both of the following conditions hold: the argument is
weak, or the argument has at least one false premise.
Constructive Dilemma: A constructive dilemma is a valid
deductive argument form of the following pattern:
(If A, then B), and/but (if C, then D).
A or C.
Therefore, B or D

12. DataTrident UniversityBUS520: Business Analytics and
Decision MakingModule 2: SLP TemplateFILL IN ALL CELLS
THAT ARE HIGHLIGHTED IN YELLOWPlease remember to
save this file with your last name in the file name. For
example: BUS520 Module 2 SLP Template,
Doe.docName:Annual Amount Spent on Organic
FoodAgeAnnual IncomeNumber of People in HouseholdGender
(0 = Male; 1 =
Female)7348771096883111598471099815192242311213941129
91381134205116556581141015011515441151005010469341163
30501793375116339601817332117907701230539119071519080
65586035191134858623416185486157921647049621802060005
76220251676071680412085794768407417393476961831816128
73079401080063759005161602477129311080066796186085432
48113140176663886246611264454891675114308288957651973
75892296401330127936145118106489395461114682695937519
54752100846407812291032762115521751041125175984510511
94077837410592531177375610608460782430108616316552571
09038201123241109585516540233783450420028389405072252
34214550537045486775144763348997412800424905811783939
49609413472605327910885457539175089004154716501279167
12630650127127313089351133215713448851880264135711401
43692413970151790825142014411784034142857601510778143
18251120703415098751638934152041216606411547023062916
21555521174255715732930114362316379451761278164108407
51536165851401311544172497511187075174458508450701775
17411632438183779509331351851114091846518646740168036
81891376010709481943515114456241943805016634461973585
01222743197400511347658198650501455466202859519393682
03591411459474206216516628322076792011240612104985013
10142210678511403460211249501783764211961617849532128
51211057862213035511132578214457507105442154422016460
58220178518390272204033114956682208935110903212212234
11205470221498511169738222618511278125229072511745630
22968561128357023022851134033723561750150514023808750
14225292407685011196542425294011475522437655156056524

13. 46252098907224520841132274024764850112003624980541960
04325203340157033825281251648673257143119430412581674
17755352586402181002126102031148215926622351106505626
62695112589422675655111600462683804113000342694314117
06570269839601650055270441508600382727952011900512748
4641167236627625050167594327723150
Question 1FILL IN ALL CELLS THAT ARE HIGHLIGHTED
IN YELLOWQUESTION 1: Generate a 95% confidence
interval for the following two variables by hand: Annual
Amount Spent on Organic Food and Age.Average Annual
Amount Spent on Organic Food (� ̅)Average Age (� ̅)t-value
from the t-table (t)t-value from the t-table (t)standard deviation
for this variable (s)standard deviation for this variable
(s)number of observations (n)number of observations (n)Margin
of ErrorERROR:#DIV/0!Margin of ErrorERROR:#DIV/0!Upper
Limit of Confidence IntervalERROR:#DIV/0!Upper Limit of
Confidence IntervalERROR:#DIV/0!Lower Limit of Confidence
IntervalERROR:#DIV/0!Lower Limit of Confidence
IntervalERROR:#DIV/0!
Questions 2-3FILL IN ALL CELLS THAT ARE
HIGHLIGHTED IN YELLOWQUESTION 2: Generate a 95%
confidence interval for the following two variables using the
Excel formula =CONFIDENCE.T(): Annual Income and
Number of People in the Household. Remember, this formula
will just give you the margin of error. You will still need to
add it to the mean and subtract it from the mean to get the upper
and lower limits of the confidence interval.margin of error from
the =CONFIDENCE.T() formulaAverage Annual IncomeUpper
Limit of Confidence Interval0Lower Limit of Confidence
Interval0margin of error from the =CONFIDENCE.T()
formulaAverage Number of PeopleUpper Limit of Confidence
Interval0Lower Limit of Confidence Interval0QUESTION 3a:
Interpret the confidence intervals for Average Annual
Income.QUESTION 3b: Interpret the confidence intervals for
Average Number of People
Question 4FILL IN ALL CELLS THAT ARE HIGHLIGHTED

14. IN YELLOWQUESTION 4: The client insists the average
income of his organic food customers is $150,000. Conduct a
hypothesis test at the 0.10 level to test his statement. What is
your decision?Step 1: State the Null and Alternate
HypothesesNull HypothesisAlternate HypothesisStep 2:
Determine Alpha (Stated in Question)0.10Step 3: Determine
Which Test Statistic Will Be UsedStep 4: Formulate a Decision
RuleStep 5: Make a Decision
Hint: This will be a 2-tail t-test.