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Logic Unit 5

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Assignment 9: Inductive Reasoning

Read Chapter 9 of the course text, then look over the below questions, and then reread the chapter with the below questions in mind. Submit your complete set of answers, i.e., answers for all assignments in the Unit, before the deadline (see syllabus).

1. Inductive probability can be increased by strengthening the _____ or weakening the _____.

Premises; conclusions

2. Evaluate the inductive probability of the below argument.

I spoke to three of my friends in the course and they all earned a D.

 Almost everyone in the course earned a D.

Weak argument, because the sample size of three is too small to justify the generalization expressed by the conclusion.

3. Give an example of a necessary and sufficient cause for an event.

Consider a situation in which a fair die is tossed once. Here are six equally likely possible outcomes: the die shows a one, denoted A1 (A subscript 2),…, and the die shows a six, denoted A6. Calculate the following probabilities:

(a). P(A1)

(b). P(~A1)

(c). P(A1  A3)

(d). P(A1 & A3)

(a). 1/6

(b). 10 - 1/6 = 5/6

(c). 2/6 = 1/3

(d). 0/6 (since the one die tossed cannot show two numbers)

4. What does ‘mutually exclusive’ mean, what is an example of mutually exclusive events, and what is the formula for calculating the probability of either of the mutually exclusive events occurring?

Mutually Exclusive: Events that cannot occur simultaneously.

Example: Prove: P(~A) = 1 – P(A)

Since A  ~A is tautologous, by Axiom 2, we have P(A  ~A) = 1.

And since A and ~A are mutually exclusive, by Axiom 3, P(A  ~A)

= P(A) + P(~A), and so P(~A) = 1 – P(A).

Formula: P (A  B) = P(A) + P(B)

5. Identify, in terms of inductive kind (“Argument by …”), and formalize, in terms of objects and properties (“Se, Ae,…”), the following argument.

Estelle is sweet, assiduous, polite, sometimes clumsy, and an insomniac.

Hernando is sweet, assiduous, polite, and sometimes clumsy.

 Hernando is an insomniac.

Humean Argument

For Questions 6-10 consult the Fallacy List (posted by the Syllabus). Fallacies, roughly, are popular mistakes of a logical sort in which logical reasons for accepting a conclusion are lacking and instead other factors are brought into play. The Fallacy List names and briefly describes the general patterns of some of these typical mistakes.

For each of the following passages, identify (in your words if necessary or desired) the conclusion (i.e., "the bottom line") of the passage and then evaluate the proposed reason in the passage for that conclusion. If a fallacy is committed, write the name of the fallacy in the "Fallacy:" space provided below the passage. If no fallacy is committed, write "No fallacy" in that space.

Example: According to the advertising industry, breakfast cereal is associated with trim youthfulness, athletic prowess, and vibrant good health; whiskey is associated with luxury and achievement; the automobile with romance, riches, and sex.

Conclusion: We should buy these products.

Fallacy: Ad populum (indirect version)

6. Julie to Mary: “If you don’t love your boyfriend anymore, then just dump him without explaining anything.”

Conclusion: Dump your boyfriend.

Fallacy: Argumentum ad Populum (direct)

7. It would be unconstitutional to outlaw sawed-off shotguns because the Second Amendment protects the right to bear arms.

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