Question 3: In a classic Conan Doyle story, Sherlock Holmes solves a crime mystery by recognizing that a guard dog didn’t bark. Therefore, the dog must have known the perpetrator. Holmes’ reasoning goes like this: if the guard dog doesn’t know a person, then it barks. The dog didn’t bark. Therefore, it knew the person. Which rule of inference is being used here?

Solution: p = guard dog doesn’t know person; not p = dog knows person; q = dog barks. If not q then not p. Not q is true. Therefore, not p is true.

- Addition
- Hypothetical Syllogism
- Simplification
- Modus Ponens
- Resolution
- Conjunction
- Disjunctive Syllogism
- Modus Tollens – Correct answer

Question 4: Which rule of inference is being used in the following argument?

If we had fusion power, then we could have spacecraft that travel at 10% light speed. If we had spacecraft that travel at 10% light speed, we could send probes to other stars. Therefore, if we had fusion power, we could send probes to other stars.

Solution: p = fusion power; q = 10% light speed; r = probe stars. If p then q. If q then r. Therefore, if p then r.

- Resolution
- Modus Ponens
- Simplification
- Addition
- Hypothetical Syllogism – Correct answer
- Modus Tollens
- Conjunction
- Disjunctive Syllogism

Question 5: The writers for a TV show have determined that they need to add a new character. One demographic wants the new character to be a man, or someone who can do martial arts. Another demographic wants the new character to be a woman, or someone who is a medical doctor. The writers wants the new character will be someone who can do martial arts or is a medical doctor. Which rule of inference was used here?

Solution: p = man; not p = woman; q = martial arts; r = medical doctor. P or q and not p or r. Therefore, q or r.

- Modus Ponens
- Simplification
- Resolution – Correct answer
- Addition
- Hypothetical Syllogism
- Modus Tollens
- Conjunction
- Disjunctive Syllogism

Question 6: Is the following argument valid, or is it a fallacy? If it is valid, identify the argument form.

Germans like bratwurst. Mike isn’t German. Therefore, Mike doesn’t like bratwurst.

Solution: p = German, q = bratwurst. If p then q and not p, so not q is a fallacy of denying the hypothesis.

- Modus Tollens
- Modus Ponens
- Fallacy – Correct answer

Question 7: Is the following argument valid, or is it a fallacy? If it is valid, identify the argument form.

Germans like bratwurst. Mike likes bratwurst. Therefore, Mike is German.

Solution: p = German; q = bratwurst. If p then q and q, therefore p is a fallacy of affirming the conclusion.

- Modus Ponens
- Fallacy
- Modus Tollens