Practice Exercises: Chapter 3

Group 1: Identifying Deduction and Induction

Identify whether each of the following arguments is Deductive (aiming for certainty) or Inductive (aiming for probability).

1. If it is a square, it has four sides. This shape is a square. Therefore, it has four sides.

2. Every time I have eaten at that restaurant, the food has been excellent. Therefore, the next time I eat there, the food will likely be excellent.

3. Eighty percent of the registered voters in this district support the new bond. Maria is a registered voter in this district. Therefore, Maria supports the bond.

4. All humans are mortal. Socrates is a human. Therefore, Socrates is mortal.

5. The last three movies by this director were thrillers. I bet the one coming out next month is a thriller too.

Group 2: Evaluating Validity and Soundness

For these Deductive arguments, determine if they are Valid or Invalid. If valid, determine if they are Sound or Unsound.

6. All birds can fly. Penguins are birds. Therefore, penguins can fly.

7. If the battery is dead, the car won’t start. The car won’t start. Therefore, the battery is dead.

8. Either the cat is on the mat or it is in the garden. The cat is not in the garden. Therefore, the cat is on the mat.

9. All cats are mammals. All mammals are animals. Therefore, all cats are animals.

10. If I am in Seattle, I am in Washington. I am in Washington. Therefore, I am in Seattle.

Group 3: Evaluating Strength and Cogency

For these Inductive arguments, determine if they are Strong or Weak. If strong, determine if they are Cogent or Uncogent.

11. Most people in the United States speak English. John is a person in the United States. Therefore, John speaks English.

12. I saw a black cat today, and then I stubbed my toe. Therefore, black cats cause bad luck.

13. Statistics show that 99% of people who take this vaccine do not get the virus. Sarah took the vaccine. Therefore, Sarah will not get the virus.

14. Every swan I have ever seen is white. Therefore, all swans in existence are white.

Group 4: Identifying Logical Patterns and Fallacies

Identify the specific form or fallacy (Modus Ponens, Modus Tollens, Disjunctive Syllogism, Affirming the Consequent, or Denying the Antecedent).

15. If it rains, the game is canceled. It is raining. Therefore, the game is canceled.

16. If I win the lottery, I will buy a boat. I didn’t buy a boat. Therefore, I didn’t win the lottery.

17. If you are a doctor, you went to medical school. You went to medical school. Therefore, you are a doctor.

18. Either we take the stairs or the elevator. We aren’t taking the stairs. Therefore, we are taking the elevator.

19. If it snows, the roads are slippery. It didn’t snow. Therefore, the roads are not slippery.

Group 5: Argument Mapping & Venn Diagrams

20. In an Argument Map, what is the difference between a co-premise and an independent reason?

21. When using a Venn Diagram to test a categorical statement like “No A are B,” what visual action do you take within the overlapping circles?

Answer Key

Group 1

1. Deductive (The conclusion follows necessarily from the definitions).

2. Inductive (Based on past experience/probability).

3. Inductive (Based on a statistical majority).

4. Deductive (Classic syllogistic form).

5. Inductive (Predicting the future based on a pattern).

Group 2

6. Valid but Unsound (The structure is perfect, but the premise “All birds can fly” is factually false).

7. Invalid (Fallacy of Affirming the Consequent; the car might not start for other reasons).

8. Valid (Disjunctive Syllogism). If the premises are true, it is Sound.

9. Valid and Sound (The structure is correct and the premises are true).

10. Invalid (Fallacy of Affirming the Consequent; you could be in Spokane).

Group 3

11. Strong and Cogent (The statistical probability is high and the premises are true).

12. Weak (Hasty generalization based on a single, likely coincidental event).

13. Strong and Cogent (High probability based on established data).

14. Strong but Uncogent (It is strong based on the evidence available to the speaker, but technically uncogent because black swans do exist).

Group 4

15. Modus Ponens (Valid).

16. Modus Tollens (Valid).

17. Affirming the Consequent (Invalid).

18. Disjunctive Syllogism (Valid).

19. Denying the Antecedent (Invalid).

Group 5

20. Co-premises work together as a single unit to support a conclusion; if one is removed, the support fails. Independent reasons each provide support on their own, regardless of the other.

21. You shade the overlapping area between circle A and circle B to show that the set of things that are both A and B is empty.