# Logic Text Chapter 2 Solutions

## Chapter 2: Connectives and Argument Forms

### Solutions

Question {2.1}

1. Greg is in town.

2. Fred is very smart.

3. Minh is a bad student

4. Every car is fuel efficient.

5. That car is either red or a diesel. (This is a tricky one. The answer is not “That car is both red and a diesel.” Do you understand why? )

Question {2.2}

1. It is -5 degrees. The clouds are grey.

2. He was tired. He wanted to keep going.

3. The waves were breaking. The surf was low.

4. There was a strike. The power was not cut.

5. Fred is not a mechanic. Jack is not a mechanic.

Question {2.3}

1. Eric is there. Yukiko is there.

2. The car is white. The car is yellow.

3. Brian is doing a Ph.D.

Brian is doing a Masters degree.

4. It rains. It doesn’t rain.

5. I’ll have coffee. I’ll have tea.

Question {2.4}

1. It is raining. I’ll walk home.

2. You look outside. (Perhaps better: You will look outside, to match the consequent.) You’ll see the nice garden I planted.

3. I’m tired. I don’t do my logic well.

4. I do logic well. I’m awake. (Be careful with “only if"s.)

5. I’m awake. I do logic well.

6. You work hard. You will pass.

7. The world’s future will be assured. We get rid of nuclear weapons.

8. We get rid of nuclear weapons. The world’s future will be assured.

9. Oswald didn’t shoot Kennedy. Someone else did shoot Kennedy.

10. Oswald didn’t shoot Kennedy. Someone else did shoot Kennedy. (This is a tricky one. “Oswald hadn’t shot Kennedy” is not a sentence, so it can’t be an antecedent, given our definition. Most people think that 9 and 10 have the same antecedent and consequent, but the conditional combines them slightly differently. In the first case we wonder what happens if Oswald isn’t Kennedy’s assassin. In the second, we assume that Oswald was Kennedy’s assassin and wonder how things would have been had he not shot Kennedy.)

Question {2.5}

1. Conditional of “Christine is happy” and “She is not thinking about her thesis”. The second proposition here is a negation of “she is thinking about her thesis.”

2. Negation of “I know if she’s coming to the party”, and this is not a conditional. (If it were, what would be the antecedent and consequent?)

3. Conditional with antecedent of “Theodore is enrolled in PHIL134, and he passes” and consequent “He can go on to do advanced logic subjects.” The antecedent is a conjunction of “Theodore is enrolled in PHIL134” and “Theodore passes PHIL134”.

4. Conditional with antecedent “Theodore isn’t enrolled in PHIL134, or he doesn’t pass” (the “if” in there can be taken out) and consequent “Theodore cannot go on to do advanced logic subjects”. The antecedent is a disjunction of “Theodore isn’t enrolled in PHIL134” (which is in turn, the negation of “Theodore is enrolled in PHIL134”) and of “Theodore doesn’t pass PHIL134” (which is in turn the negation of “Theodore does pass PHIL134”). The consequent, which is, remember, “Theodore cannot go on to do advanced logic subjects”, is the negation of “Theodore can go on to do advanced logic subjects”. Phew!

5. This is the conjunction of “I believe that you are either going to leave the party early or make a scene” and “You know that you are either going to leave the party early or make a scene”. These both don’t go any further. The first is an “I believe that …” statement. This is not a disjunction of “I believe that you are going to leave the party early” and “I believe that you are going to make a scene”, as I might not believe either disjunct of the disjunction, while still believing the whole disjunction. Same goes for the other conjunct about knowledge.

Question {2.6}

1. Yukiko is not a linguist.

2. Yukiko is not a linguist or Pavlos is a logician.

3. Yukiko is not a linguist if and only if Christine is a lawyer.

4. If Yukiko is a linguist, then if Christine is a lawyer, Pavlos is a logician.

5. If Yukiko is a linguist and Pavlos is not a logician then Christine is a lawyer.

6. Yukiko is a linguist and Christine is a lawyer.

7. It’s not the case that both Yukiko is a linguist and Pavlos is a logician.

8. It’s not the case that Yukiko is a linguist if and only if Christine is a lawyer.

9. It’s not the case that Christine is not a lawyer.

10. Yukiko is a linguist if and only if either Christine is a lawyer or Pavlos is not a logician.

11. Yukiko is a linguist or Christine is a lawyer.

12. Yukiko is a linguist if and only if Pavlos is a logician.

13. If Yukiko is a linguist, Christine is a lawyer.

14. If Yukiko is a linguist only if Christine is a lawyer, then Pavlos is a logician.

15. I can’t get a good English translation for this. Can you?

Question {2.7}

1. ~ c

2. y & p

3. py

4. p ∨ ~ y

5. ~(p & c)

6. y ⊃ (p & ~ c)

7. (y ∨ ~ p) ⊃ c

8. y ≡ (p ∨ ~ c)

9. p ∨ (yc)

10. (py) ⊃ c

Question {2.8}

1, 4, 6, 9 and 10 are well-formed, the rest are not.