Logically, it's the only solution.

Two days ago, I wrote an entry about Judge Aldisert's book, Logic for Lawyers. Included in that entry was a logic problem from Chapter 3 of the book. Ashley Morris solved the problem. Below the fold, I'm going to prove logically that Ashley's solution is not only correct, but also the only logical solution to the problem.

For lawyers, the proof of the solution is as important as the solution itself. Our job as lawyers is not only to figure out the solution to a legal problem, but also to convince others (clients, opponents, judges) that our solution is correct. We can't do that unless we explain our reasoning step by step, showing that each step is grounded in fact, not speculation. If you want to see my attempt to prove Ashley's solution, continue reading.

First, make a couple of grids: one for subjects taught; the other for law schools attended.

_|Wis|Wis|Va.|Pit|Pen|Har|

A|   |   |   |   |   |   |

B|   |   |   |   |   |   |

C|   |   |   |   |   |   |

D|   |   |   |   |   |   |

E|   |   |   |   |   |   |

F|   |   |   |   |   |   |

 

| Admin|Contr|Evid.|Torts|Crime|CivPr|

A|     |     |     |     |     |     |

B|     |     |     |     |     |     |

C|     |     |     |     |     |     |

D|     |     |     |     |     |     |

E|     |     |     |     |     |     |

F|     |     |     |     |     |     |

The following facts are given; we’ll number them to make them easier to refer to below when we draw deductions from them:

1. The group comprises six law-school professors.

2. All six group members teach at Pitt.

3. Two group members graduated from Wisconsin.

4. Of the non-Wisconsin grads, one graduated from Va., one from Pitt, one from Penn, and one from Harvard.

5. One member of the group teaches administrative law; one teaches contracts; one teaches evidence; one teaches torts; one teaches crimes; and one teaches civil procedure.

6. The Harvard grad teaches civil procedure.

7. The Harvard grad lives in the same apartment house as Easy.

8. Easy does not teach evidence, torts, administrative law, or crimes.

9. Charlie teaches evidence.

10. The contracts teacher is Charlie’s law-school classmate.

11. Charlie and the contracts teacher attended their law-school reunion.

12. Dogge’s alma mater is Pitt.

13. Able teaches administrative law.

14. Foxx has never attended a class reunion.

15. Foxx does not teach torts.

16. Foxx did not go to Harvard.

17. Foxx did not go to any law school located in Pennsylvania.

18. Neither Able nor the torts professor attended Harvard.

19. Able did not attend Pitt.

20. The torts professor did not go to Penn.

From these premises, we can deduce the following:

 21. Because Easy and the Harvard grad are two different people (Fact # 7), Easy is not the Harvard grad.

22. Because Charlie and the contracts teacher are two different people (Fact # 11), Charlie is not the contracts teacher.

23. Because Able and the torts professor are two different people (Fact # 18), Able is not the torts professor.

Let’s fill in the grids based on what we now know. A dot means “true,” and X means “false,” and the number after the dot or the X denotes the corresponding proven statement.

_|Wis|Wis|Va.|Pit|Pen|Har|

A|   |   |   |x19|   |x18|

B|   |   |   |   |   |   |

C|   |   |   |   |   |   |

D|   |   |   |•12|   |   |

E|   |   |   |   |   |x21|

F|   |   |   |   |   |x16|

 

| Admin|Contr|Evid.|Torts|Crime|CivPr|

A| •13 |     |     | x23 |     |     |

B|     |     |     |     |     |     |

C|     | x22 |  •9 |     |     |     |

D|     |     |     |     |     |     |

E| x8  |     | x8  | x8  | x8  |     |

F|     |     |     | x15 |     |     |

Since we know that Dogge is the Pitt grad, we can logically eliminate the other five group members as Pitt grads. The syllogism is simple:

Premise: Only one of the six group members graduated from Pitt (Fact # 4).

Premise: Dogge is the group member who graduated from Pitt (Fact # 12).

Fact # 24: Therefore, no other group member graduated from Pitt.

 

By applying the same logic horizontally (according to our grid), we can rule out Dogge as a graduate of any law school other than Pitt.

Premise: Dogge graduated from only one law school (Fact # 4).

Premise: That one law school is Pitt (Fact # 12).

Fact # 25: Therefore, Dogge did not graduate from any of the other law schools.

 

By similar logic, we can reach the following conclusions:

Fact # 26: Because Able teaches administrative law (Fact # 13), no other group member teaches administrative law.

Fact # 27: Because Able teaches administrative law (Fact # 13), he does not teach any other subject.

Fact # 28: Because Charlie teaches evidence (Fact # 9), no other group member teaches evidence.

Fact # 29: Because Charlie teaches evidence (Fact # 9), Charlie does not teach any other subject.

_|Wis|Wis|Va.|Pit|Pen|Har|

A|   |   |   |x19|   |x18|

B|   |   |   |x24|   |   |

C|   |   |   |x24|   |   |

D|x25|x25|x25|•12|x25|x25|

E|   |   |   |x24|   |x21|

F|   |   |   |x24|   |x16|

 

| Admin|Contr|Evid.|Torts|Crime|CivPr|

A| •13 | x27 | x27 | x23 | x27 | x27 |

B| x26 |     | x28 |     |     |     |

C| x26 | x22 |  •9 | x29 | x29 | x29 |

D| x26 |     | x28 |     |     |     |

E| x8  |     | x8  | x8  | x8  |     |

F| x26 |     | x28 | x15 |     |     |

Now, look at the right-hand column in both grids, remembering that the Harvard grad teaches civil procedure. The grids show that Baker must be the Harvard grad and the civil-procedure teacher. In syllogistic terms:

Premise: The Harvard grad teaches civil procedure (Fact # 6).

Premise: All group members except Baker and Charlie have been ruled out as Harvard grads (Facts # # 16, 18, 21, and 25).

Premise: Charlie cannot be the civil procedure teacher (Fact # 29).

Fact # 30: Therefore, Baker must be the Harvard grad and the civil-procedure teacher.

Fact # 31: Since Baker is the Harvard grad (Fact # 30), Charlie cannot be the Harvard grad.

Fact # 32: Since Baker graduated from Harvard, Baker did not graduate from any of the other law schools.

Fact # 33: Since Baker teaches civil procedure (Fact # 30), no one else is the civil-procedure teacher.

Fact # 34: Since Baker teaches civil procedure (Fact # 30), Baker does not teach any other course. 

_|Wis|Wis|Va.|Pit|Pen|Har|

A|   |   |   |x19|   |x18|

B|x32|x32|x32|x24|x32|•30|

C|   |   |   |x24|   |x31|

D|x25|x25|x25|•12|x25|x25|

E|   |   |   |x24|   |x21|

F|   |   |   |x24|   |x16|

 

| Admin|Contr|Evid.|Torts|Crime|CivPr|

A| •13 | x27 | x27 | x23 | x27 | x27 |

B| x26 | x34 | x28 | x34 | x34 | •30 |

C| x26 | x22 |  •9 | x29 | x29 | x29 |

D| x26 |     | x28 |    |      | x33 |

E| x8  |     | x8  | x8 | x8   | x33 |

F| x26 |     | x28 | x15 |     | x33 |

We can now plainly see that Dogge is the torts teacher.

Fact # 35: Since only one member of the group can be the torts teacher (Fact # 5), and since all group members except Dogge have been eliminated as torts teacher (Facts # # 8, 15, 23, 29, and 34), Dogge must be the torts teacher.

Fact # 36: Since Dogge teaches only one subject (Fact # 5), and since that subject is torts (Fact # 35), Dogge does not teach any other subject.

Fact # 37: Since the torts teacher did not attend Penn, and since Dogge is the torts teacher, Dogge did not attend Penn (but we already knew that – see Fact # 25).

 

_|Wis|Wis|Va.|Pit|Pen|Har|

A|   |   |   |x19|   |x18|

B|x32|x32|x32|x24|x32|•30|

C|   |   |   |x24|   |x31|

D|x25|x25|x25|•12|x25|x25|

E|   |   |   |x24|   |x21|

F|   |   |   |x24|   |x16|

 

| Admin|Contr|Evid.|Torts|Crime|CivPr|

A| •13 | x27 | x27 | x23 | x27 | x27 |

B| x26 | x34 | x28 | x34 | x34 | •30 |

C| x26 | x22 | •9  | x29 | x29 | x29 |

D| x26 | x36 | x28 | •35 | x36 | x33 |

E| x8  |     | x8  | x8  | x8  | x33 |

F| x26 |     | x28 | x15 |     | x33 |

We can also deduce that Charlie attended Wisconsin. But to ensure the validity of this conclusion, let’s make our reasoning explicit:

Premise: Two members of our group share the same alma mater, as both went to the same reunion.

Premise: Wisconsin is the only school on the grid with two graduates in our group of professors.

Fact # 38: Therefore, the two group members who attended the reunion must be Wisconsin alumni.

 

Premise: The two who attended the reunion are Wisconsin alumni (Fact # 38).

Premise: One of those two is Charlie (Fact # 11).

Fact # 39: Therefore, Charlie must have graduated from Wisconsin.

Fact # 39a: Since Charlie can be only one of the two Wisconsin grads, we rule her out as the other Wisconsin grad.

Fact # 40: Since Charlie graduated from Wisconsin, she did not graduate from any of the other law schools.

 

_|Wis|Wis|Va.|Pit|Pen|Har|

A|   |   |   |x19|   |x18|

B|x32|x32|x32|x24|x32|•30|

C|•39|39a|x40|x24|x40|x31|

D|x25|x25|x25|•12|x25|x25|

E|   |   |   |x24|   |x21|

F|   |   |   |x24|   |x16|

 

| Admin|Contr|Evid.|Torts|Crime|CivPr|

A| •13 | x27 | x27 | x23 | x27 | x27 |

B| x26 | x34 | x28 | x34 | x34 | •30 |

C| x26 | x22 | •9  | x29 | x29 | x29 |

D| x26 | x36 | x28 | •35 | x36 | x33 |

E| x8  |     | x8  | x8  | x8  | x33 |

F| x26 |     | x28 | x15 |     | x33 |

While we’re thinking about that Wisconsin reunion, let’s file one more syllogism away for future reference:

Premise: The two group members who attended the reunion are Wisconsin alumni (Fact # 38).

Premise: One of those two teaches contracts (Fact # 11).

Fact # 41: Therefore, the contracts teacher attended Wisconsin.

Fact # 42: Therefore, anyone who attended a law school other than Wisconsin can be ruled out as the contracts teacher.

Looking at our grids, we realize that we’ve identified Foxx as the crimes professor:

Premise: One and only one group member is the crimes teacher (Fact # 5).

Premise: All group members except Foxx have been ruled out as the crimes professor (Facts # # 8, 27, 29, 34, and 36).

Fact # 43: Therefore, Foxx is the crimes professor.

Fact # 44: Since Foxx teaches crimes, Foxx does not teach any other subject.

We can now rule out Foxx as a Wisconsin grad:

Premise: Two and only two group members graduated from Wisconsin (Fact # 3).

Premise: One of those two is Charlie (Fact # 39).

Premise: The other is the contracts professor (Fact # 41).

Premise: Foxx is not Charlie (self-evident).

Premise: Foxx is not the contracts professor (Fact # 44).

Fact # 45: Therefore, Foxx did not attend Wisconsin.

 

_|Wis|Wis|Va.|Pit|Pen|Har|

A|   |   |   |x19  | |x18|

B|x32|x32|x32|x24|x32|•30|

C|•39|39a|x40|x24|x40|x31|

D|x25|x25|x25|•12|x25|x25|

E|   |   |   |x24|   |x21|

F|x45|x45|   |x24|   |x16|

 

| Admin|Contr|Evid.|Torts|Crime|CivPr|

A| •13 | x27 | x27 | x23 | x27 | x27 |

B| x26 | x34 | x28 | x34 | x34 | •30 |

C| x26 | x22 | •9  | x29 | x29 | x29 |

D| x26 | x36 | x28 | •35 | x36 | x33 |

E| x8  |     | x8  | x8  | x8  | x33 |

F| x26 | x44 | x28 | x15 | •43 | x33 |

We now see that Easy must be the contracts professor, which also makes Easy our other Wisconsin grad. 

Premise: One member of the group teaches contracts (Fact # 5).

Premise: All members of the group except Easy have been eliminated as the contracts teacher (Facts # # 22, 27, 34, 36, and 44).

Fact # 46: Therefore, Easy is the contracts professor.

 

Premise: The contracts professor graduated from Wisconsin (Fact # 41).

Premise: Easy is the contracts professor (Fact # 46).

Fact # 47: Therefore, Easy graduated from Wisconsin.

Fact # 47a: Since Easy can be only one of the two Wisconsin grads, we rule him out as the other one.

Fact # 48: Since Easy graduated from Wisconsin (Fact # 47), Easy did not graduate from any other law school.

 

Now that we have identified both Wisconsin grads, we can rule out Able as a Wisconsin grad.

Premise: Only two members of the group are Wisconsin grads (Fact # 3).

Premise: One of those two members is Charlie (Fact # 39).

Premise: The other is Easy (Fact # 37).

Premise: Able is not Charlie, and Able is not Easy (self-evident).

Fact # 49: Therefore, Able is not a Wisconsin grad.

 

_|Wis|Wis|Va.|Pit|Pen|Har|

A|x49|x49|   |x19|   |x18|

B|x32|x32|x32|x24|x32|•30|

C|•39|39a|x40|x24|x40|x31|

D|x25|x25|x25|•12|x25|x25|

E|47a|•47|x48|x24|x48|x21|

F|x45|x45|   |x24|   |x16|

 

| Admin|Contr|Evid.|Torts|Crime|CivPr|

A| •13 | x27 | x27 | x23 | x27 | x27 |

B| x26 | x34 | x28 | x34 | x34 | •30 |

C| x26 | x22 |  •9 | x29 | x29 | x29 |

D| x26 | x36 | x28 | •35 | x36 | x33 |

E|  x8 | •46 | x8  | x8  | x 8 | x33 |

F| x26 | x44 | x28 | x15 | •43 | x33 |

We’re almost home: 

Premise: Foxx did not attend a law school located in Pennsylvania (Fact # 17).

Premise: Penn is located in Pennsylvania (you can look it up on Google maps.)

Fact # 50: Therefore, Foxx did not attend Penn.

 

Premise: One member of the group graduated Penn (Fact # 4).

Premise: All members of the group except Able have been eliminated as Penn grads (Facts # # 25, 32, 40, 49, and 50).

Fact # 51: Therefore, Able must have graduated from Penn.

Fact # 52: Because Able graduated from Penn, he did not graduate from Virginia.

 

 

Premise: One member of the group graduated from Virginia (Fact # 4).

Premise: All members of the group except Foxx have been eliminated as the Virginia grad (Facts # # 25, 32, 40, 49, and 52).

Fact # 53: Therefore, Foxx must be the Virginia grad.

 

 Alternatively:

Premise: Foxx graduated from one of the five law schools (Facts # # 3 and 4).

Premise: Every law school except Virginia has been eliminated as Foxx’s alma mater (Facts # # 16, 24, 45, and 50).

Fact # 53: Therefore, Foxx must have graduated from Virginia.

 

_|Wis|Wis|Va.|Pit|Pen|Har|

A|x49|x49|x52|x19|•51|x18|

B|x32|x32|x32|x24|x32|•30|

C|•39|39a|x40|x24|x40|x31|

D|x25|x25|x25|•12|x25|x25|

E|47a|•47|x48|x24|x48|x21|

F|x45|x45|•53|x24|x50|x16|

 

| Admin|Contr|Evid.|Torts|Crime|CivPr|

A| •13 | x27 | x27 | x23 | x27 | x27 |

B| x26 | x34 | x28 | x34 | x34 | •30 |

C| x26 | x22 |  •9 | x29 | x29 | x29 |

D| x26 | x36 | x28 | •35 | x36 | x33 |

E|  x8 | •46 |  x8 |  x8 |  x8 | x33 |

F| x26 | x44 | x28 | x15 | •43 | x33 |

We now have the problem solved:

Able – Penn –  administrative law.

Baker – Harvard – civil procedure.

Charlie – Wisconsin – evidence.

Dogge – Pitt – torts.

Easy – Wisconsin – contracts.

Foxx – Virginia – crimes.

More importantly, we’ve proven through logic that this solution is the only solution.