w6

L1        (L2)

EXAM: Soon

Class will resume after 1 hour (we'll take roll and do important stuff--a big step):

Derivations

 

 

 

 

 

 

 

 

 

 

 

I. Review?

  1. Tables with n-atomic sentences.
  2. Concepts
  3. only if, neither, etc.
  4. Homework?

 

 

II. Exam

  1. Do all problems...go for extra credit.
  2. All answers go on the white paper.
  3. There are different exam versions...don't copy. No books, no notes...
  4. In the one "like 3.1", do one row tables.
  5. In 7, the handout doesn't show metavariables P and Q well.

next...

 

 

 

 

 

 

 

 

 

w6 (continued)

roll

next exam: two weeks! We need to get busy!

 

 

 

 

 

 

 

 

Exam Answers...

 

 

 

 

III. Derivations

 

Who are Holmes and Moriarity? What's Holmes so famous for? (Brilliant ....  Elementary my dear... )

 

 

 

 

Think about our longer argument (oops, I removed a tilde):

                    (A&~B)>C
                        A&~B
                         C&A

Maybe this is:

If Arthur is a student and Barb is not, then she's been cheated. Since it turns out that Arthur is a student and Barb is not, it follows that she's been cheated as well as that he's a student.

B. How should we more easily think of this?   Step-by-step:

 

C. Rules

  1. The first step in the reasoning puts two ideas together:








  2. Lots of easy inferences have this form:








  3. We can see formulate this rule as follows:









  4. So we can name rules , look again...

 

 

 

 

 

 

 

 

 

 

  5. Let's do this one more formally...

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

L2

roll

exam return -5 = A-, -10 = B-, -15 = C-, -20 = D-

next exam: 12 days! We need to get busy!

Office Hours: T 12-1:30, Th 2-3 and by appointment. My Tuesday OH sometimes run a little late because I'm in another class.

 

 

 

 

 

 

 

 

I. Review:

  1. rules? What was that rule name... > what?









  2. How do we know this is valid?













  3. Other rules?











  4. Let's do some.










  5. You Do:
      • From K>(J&L) and K, derive L
      • From K>J and (K>R)&F derive J&F

 

 

 

II. More rules...

  1. = is called the biconditional because?


  2. So the following little arguments are valid.








  3. Our new rules simply follow these validities:












  4. So, for examples.









  5. v-rules
    • What would you need to know, in order to be certain that at least one of Ken and Beth is from Minnesota? What ONE thing about Beth would you need to know to be sure that the disjunction is true?



















    • Now, how should we think about v-I???

























     

     


     

  6. More Problems...










  7. Your Problems
    A. A=B,B>C,A&L / C&L  (i.e., from the first three derive 'C&L')
    B. (AvB)=C,B&L / C
    C. (AvB)=C,C&L / AvB
    D. AvB,A>J,(B>J)&R / J

next...

 

 

 

 

 

 

 

 

 

 

 

 

 

III. Conditional Introduction

  1. How do we prove a conditional in informal proofs? We begin with what word?






  2. Example:










  3. Informal proof:

    If an argument is sound, then it does not have a false premise .      fill in...


  4. How will we put this "suppose" into our derivations? Let's do some...









  5. Oh and here's that rule...