L1 W8       (L2)

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exam soon (thirty minutes); class resumes at 3:45

 

 

 

 

I. Exam preview

  • 1.
    Make assumptions only for >I
  • 2.
    Pitfalls:
    • Despair (and assuming what will work): "Don't assume"
    • E,I rules used on what is not the main connective
    • Citing the wrong number of inputs, e.g., "3 >E".
    • Random rule application
    • Citing from within a terminated subderivation

 

 

 

II. Exam

(next)

 

 

 

 

 

 

 

 

 

 

 

 

 

III. Strategy

  1. Suppose you are trying to derive [F&~(CvD)]>(Fv~D) to show it's a logical truth.
    • 1.

    • 2.



    • 3.



    • 4.




    • 5.










  2. Let's try it (and some more)








           (next)

 

 

 

 

 

 

IV. Short-cuts (A.K.A. SD+)

  1. We will add three further rules of inference. We don't really need to. But each will shorten proofs. Let's see how this works.






  2. Notice:






  3. Here are the formal statements of the rules:















  4. Finally, you should try some (the premises go before the slash, the goal after the slash):
    • Kv~S,~K&(JvS) / J
    • (L&M)>J, J>(TvS) / (L&M)>(TvS)
    • (J&K)>(TvS), (TvS)>K / ~K>~(J&K)


      (computer version of these three)









  5. But our most powerful new rules involve what are called

























































  6. Here's what DM looks like ; the double arrow indicates equivalence. Notice that there are two versions. We just used the second; what does the first remind you of?






















  7. More next time!

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

L2w8

roll

exam return

exams every two weeks!!! Next one: November 2.

 

 

 

 

 

 

I. Strategy Review

  1. Strategy Guidelines



  2. Presentations (don't forget to do the tutorials...there's lots of explanation there!)




  3. Concepts and Strategy for more complex derivations
    • Sometimes we need to make a subderivation within a subderivation. Think about proving that 'K>(J>(K&J))' is logically true. You'd begin by assuming what?






















    • Let's do some

(next)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

II. SD+ Revisited

    Remember our SD+ Rules of Inference?






















  1. Finish a problem set: problems 4 and 5





  2. But our most powerful new rules involve what are called































  3. There are lots of other rules of inference. They all make sense and all are dispensible. Still, they make good short-cuts. Here are three more:










































































  4. Distribution
    • Suppose we know that (a) we will go to Colorado this summer and (b) we will either climb Mount Evans or raft the Arkansas. In symbols...
























    • This helps exlain our new rule


















  5. Homework






  6. Here's a rule that is self explanatory: Equivalence












  7. And a few final rules...














  8. Homework

    5.7ex IV

    1. From the following premises:
          ~S>~T
          ~(T>S)vL

     derive: L

    2. From the following premise:
          A>(A>E)

     derive: A>E


    3. From the following premises:
          ~(P=Q)
          ~(P&Q)>(~R&~S)

     derive: ~(RvS)


    4. From the following premise:
          (~S&G)v(~S&K)

     derive: (KvG)&~S


    5. From the following premises:
          L&(S>T)
          ~(L&T)

     derive: L&~S