## exercises study 4: more argument forms

**Exercise 4.1 Additional Argument Forms**

Instructions: Fill in the blanks in each statement with the letter of the correct answer.

- a. disjunctive syllogism
- b.. affirming the consequent
- c. complete
- d. denying the antecedent
- e. dilemma
- f. transitive syllogism
- g. modus ponens
- h. modus tollens
- i. interdefinable
- j. valid

*STATEMENTS:*

1. _____ has an implication as a premise and the antecedent of the implication as a second premise from which one concludes the consequent of the first.

2. The form of argument in which: X implies Y, and the 2nd premise is: Y is false; and the conclusion is therefore: X is false, is known as _____.

3. "X implies Y, and Y is true; therefore, X is true." This argument form exemplifies the fallacy of _____.

4. Argument Form: X implies Y, and X is false; therefore, Y is false, is the fallacy of _____.

5. The _____ form consists of premises: X + Y, and X is false, to conclude: Y is true.

6. The argument form [(X < Y) (Z < W) (X + Z)] < (Y + W) is known as a(n) _____.

7. If the first two premises of a dilemma are not _____ inferences, the dilemma fails.

8. The disjunction premise of a dilemma must be a _____ disjunction or the dilemma fails.

9. The formula: (XY)' = (X' + Y') shows that conjunction and disjunction are _____.

10. The implication [(X < Y) (Y < Z)] < (X < Z) is known as _____.

**Exercise 4.2 Arguments & Definitions**

Instructions: Determine the validity of each of the following.

1. If the party now in power wins the next election, then in all probability we shall go to war somewhere in the world. In all probability we shall go to war somewhere in the world. Therefore, the party now in power wins the next election.

2. If Jane is a good speller, then she can spell "syllogism." Jane is not a good speller. Therefore, Jane cannot spell "syllogism."

3. If students cheat on exams, this means the exams are too difficult. If the exams are too difficult, the instructor should be disqualified. Therefore, if students cheat on exams, the instructor should be disqualified.

4. If John stole the money, then he has a guilty conscience. He stole the money. Therefore, he has a guilty conscience.

5. If she is honest, she will not lie. She did not lie. Consequently, she is not dishonest.

6. Either this course is easily mastered, or it should not be listed in General Education. Either this course should be listed in General Education, or it should be abolished from the entire curriculum. Therefore, if this course is not easily mastered, it should be abolished from the entire curriculum.

7. If you do nothing, then you will be considered an accomplice. If you resist, then you will be accused of provoking disagreement. Either you do nothing, or you resist. Thus, either you will be considered an accomplice, or you will be accused of provoking disagreement.

8. Either this beaker does not contain acid, or it will turn litmus paper red. It does not turn blue litmus paper red. Therefore, the beaker does not contain acid.

9. If A then B is equivalent to Not-A or B is equivalent to it is Not the case that both A and not-B.

10. The denial of

*A*

*+ B*is equivalent to both

*Not-A and Not-B*; and the

*denial of both A and B*is equivalent to

*either Not-A or Not-B*.

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