4.1ex I Basic Symbolizations

Use the following interpretation and symbolize each of the following in the space provided:

A: Ames is a politician.
B: Bates is a politician.
C: Connors is a politician. D: Ames is disreputable.
E: Bates is emotional.
F: Connors is fastidious.

  1. Ames is a politician just in case he's disreputable.
  2. Neither Bates nor Connors is a politician.
  3. Ames is a politician only if he's not disreputable.
  4. Bates's being emotional is a necessary condition for her to be a politician.
  5. Connors is not both fastidious and a politician.
  6. Ames is a politician unless Connors isn't one.
  7. Ames' being a politician is a sufficient condition for him to be disreputable.
  8. Ames is disreputable if he's a politician.

4.2ex I  Hybrids for Symbolization
Do a short multiple choice exercise:

Use 'A' for "Alberta is a province", 'C' for "The Canadian administrative law has changed", 'Q' for "Quebec is a province" and 'Y' for "The Yukon is a province".

1. Which of the following gives a hybrid symbolization for
"Either Alberta or Quebec is a province only if the Yukon is not."
a. If ~Y then, (A or Q) b. (Either A or Q) if ~Y c. (Either A or Q) only if ~Y

2. Which of the following gives a hybrid symbolization for
"If neither Quebec nor Alberta is a province, then the Yukon is a province if and only if the Canadian administrative law has changed."
a. If (neither Q nor A), then (Y if and only if C). b. (Neither Q nor A) if (Y if and only if C). c. (Neither Q nor A) if and only if (if Y then C).

3. Which of the following gives a hybrid symbolization for
"If Alberta and the Yukon are not both provinces, then both Quebec and Alberta are provinces."
a. If (~A and ~Y) then (Q and A) b. If ~(A and Y) then (Q and A) c. ~A and [if Y then (Q and A)]

4.2ex II   Complex Symbolizations

Use the following interpretation and symbolize each of the following in the space provided:

A: Ames is a politician.
B: Bates is a politician.
C: Connors is a politician.
D: Ames is disreputable.
E: Bates is emotional.
F: Connors is fastidious.

You may want to write up the hybrids on paper to help your work.

  1. If either Ames or Bates is a politician, then Connors is too.
  2. Both Connors and Bates are pols only if Ames is neither disreputable nor a politician.
  3. Either Bates is emotional unless she's a politician, or Ames is no politician.
  4. Neither is being fastidious necessary for Connors to be a politician nor is being emotional sufficient for Bates to be one.
  5. If Ames is disreputable only if he's a politician, then Connors is not both a politician and fastidious.

4.2ex III   Symbolizations that Quantify

Use the following interpretation and symbolize each of the following in the space provided:

A: Ames is a politician.
B: Bates is a politician.
C: Connors is a politician.

You may want to write up the hybrids on paper to help your work.

  1. At least one of the three is a politician.
  2. At most one of the three is a politician.
  3. Exactly one of the three is a politician.
  4. Exactly three are politicians.
  5. None are politicians.
  6. If exactly one of the three is a politician, then that politician is not Ames. (Hint: copy your answer from three, paste it here, then add a bit to it!)
  7. At most two of the three are politicians.
  8. If exactly one of the three is a politician, then at least one is a politician. (Hint: this seems a difficult one until you realize that it's logically true. Then, because any logical truth is logically equivalent to any other, you may just enter the simplest logical truth you can come up with. It won't look like the English, but that's OK!)

4.3ex I   True/False and Explain

Say whether the following are true or false. Then explain your answer.

1. If it's wrong to assert a certain sentence in a certain situation, then that sentence must be false in that situation.

2. The argument "Dole is not US President, so if he is president, then he can jump over the moon" might be symbolized as '~D / D>J'. This argument is valid in SL so the original English argument is valid.

3. "She's ten or eleven" is translated as 'TvE'. The wedge is inclusive "or". Thus it must be that she can be both ten and eleven.

Chapter 4 Review Exercises   ex I
Symbolizations
The following contain easy and more difficult examples. Make sure they all make sense to you!

Use the following interpretation:

A: Ames is a politician.
B: Bates is a politician.
C: Connors is a politician.
D: Ames is disreputable.
E: Bates is emotional.
F: Connors is fastidious.

  1. Ames is a politician and he's not disreputable.
  2. Ames is a politician if and only if he's not disreputable.
  3. Ames is a politician if he's not disreputable.
  4. Ames is a politician unless he's not disreputable.
  5. Ames is a politician only if he's not disreputable.
  6. Neither Bates nor Connors is a politician.
  7. Bates and Connors aren't both politicians.
  8. Bates and Connors both aren't politicians.
  9. If both Bates and Connors are politicians, Ames is disreputable.
  10. If Bates is emotional unless Connors is a politician, then Ames is disreputable.
  11. If Bates is a politician provided Connors is not, then both are politicians.
  12. At least one of the three is a politician.
  13. Exactly one of the three is a politician.
  14. If Connors is fastidious and Bates emotional, then Connors is a politician only if Bates is not.
  15. Connors is a politician unless she is fastidious, in which case she is not a politician but Ames is.

Chapter 4 Review Exercises ex II
More Review Symbolizations
The following contain easy and more difficult examples. Make sure they all make sense to you!

Use the following interpretation:

A: Ames is a politician.
B: Bates is a politician.
C: Connors is a politician.
D: Ames is disreputable.
E: Bates is emotional.
F: Connors is fastidious.

  1. Ames is a politician if he's not disreputable.
  2. Ames is a politician only if he's disreputable.
  3. Ames is a politician although he's disreputable.
  4. Ames isn't a politician unless he's not disreputable.
  5. Ames is a politician provided he's not disreputable.
  6. Neither Bates nor Connors is a politician.
  7. Bates and Connors aren't both politicians.
  8. Bates and Connors both aren't politicians.
  9. If either Bates or Connors is a politician, Ames is disreputable.
  10. If Bates is emotional unless Connors is a politician, then Ames is disreputable if and only if he's a politician.
  11. Bates is a politician unless Connors is not, in which case neither is a politician.
  12. It's not the case that all three are politicians.
  13. Exactly one of the three is a politician, but it's not Connors.
  14. If Connors is fastidious only if Bates emotional, then Connors is a politician unless Bates is not.
  15. For Connors to be a politician it's sufficient that she is fastidious, but being emotional is a necessary condition for Bates to be a politician.