Exam 2 Study Guide

• Primarily, study the homework problems, and
  make sure you can do them.
• Study the syllogisms on page 58 of the text. 
  You should know these by name and by
  formula, and should also understand them.
• Which brings us to the third item you should
  study:  Recognizing a syllogism when you see it.
  Below, there are a few arguments, each of which
  uses a single syllogism from that table.  In each
  case, identify the syllogism, to the point of
  assigning letters to various parts of the argument
  and showing how it has the structure of the
  indicated syllogism, and therefore how Alice
  draws her conclusion from Bob's statements.
  An example is shown.

Argument	Analysis
Bob:  I'll either review disjunctive syllogism or give the quiz now.  And I'm not going to review disjunctive syllogism.  Alice:  So you will give the quiz now.	p:  I will review disjunctive syllogisms q:  I will give the quiz now We are given (p OR q) and NOT p So Alice concludes q, by disjunctive syllogism
Bob:  If I leave town for the exam, then some student will send in a friend to take his test.  If any of my students cheat, then I will be sad. Alice:  So if you leave town, you'll be sad.
Bob:  I'm tired and hungry.  Alice:  So, you're tired.
Bob:  I'm tired. Alice:  So, you're tired or hungry
Bob:  I will either study or go to the party.  On the other hand, I'm so busy that I better either skip the party or skip frisbee golf practice. Alice:  So, you'll either study or skip frisbee golf practice.
Bob:  If I loved you, I would have given you flowers.  And I don't see any flowers here... Alice:  Go away
Bob:  Solid evidence places either Sam or Sara at the scene, and someone saw Sara at Staccato that Sunday. Alice:  So Sam stole the silken sari.
Bob:  I ate the fish for lunch, and anyone who ate the fish is going to be sick this evening. Alice:  You are going to be sick this evening.
Bob:  Odd permutations can never have exactly 100 rungs in a permutation ladder, and permutation µ has exactly 100 rungs in its ladder. Alice:  So µ must be even
Bob:  If a prime number is congruent to 3 (mod 4), then it does not factor over the Gaussian integers.  Furthermore, if an odd prime number is not the sum of two squares, then it must be congruent to 3 (mod 4). Alice:  So odd primes which aren't the sum of two squares do not factor over the Gaussian integers.