Day 6: mat385

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Today:

Announcements:
- I am grading your third assignment (key -- video details): problems 13(bfj), 21(af), 36(ac)
  - #13(bfj): Odd, so it's in the back of the book. It's always nice to see some "off road" attempts, however. So, for example, on part b, several students included either
    1. $(\forall x) [D(x) \land S(x) \rightarrow R(x)]$
    2. $(\forall x) [D(x) \rightarrow (S(x) \rightarrow R(x))]$
      (Note that this illustrates the deduction method.)
    3. I don't like the answer in the back of the book (which I saw a lot):
      
      $(\forall x) [D(x) \land S(x) \rightarrow D(x) \land R(x)]$
      It's redundant: you can always throw the hypotheses of an argument into the conclusion. So its also true that
      
      $(\forall x) [D(x) \land S(x) \rightarrow D(x) \land S(x) \land R(x)]$
      even more redundant!
  - #21(af): These were relatively straightforward, and are found in the back of the book.
  - #36(ac): the biggest problem I saw was the failure to justify. Many of you simply assert. We need some reasons here. See the key, and/or listen to the explanations on the video key.
  - General things:
    1. A few scope issues. In particular, be careful of creating a new $x$ within the scope of another $x$.
      The bigger scope issue is forgetting to extend your parrentheses or brackets enough, so that a dangling $x$ becomes free.
      For example, in that wff above I might forget the brackets:
      $(\forall x) D(x) \rightarrow (S(x) \rightarrow R(x))$
      In which case the $x$ in $(S(x) \rightarrow R(x))$ is free -- is different from the $x$ referenced in the antecedent.
    2. Some of you put $\exists$ together with $\rightarrow$; or $\forall$ with $\land$. Almost never!
      Remember the problems:
      - In the domain of the integers: \[ (\exists x)(x<0 \rightarrow x>0) \]
  If you have any issues with the grading let me know. Great job getting me the pdfs in legible formats! I am mostly interested in you trying the problems. (The answers are available in the back of the book or on the web -- I know! I've probably seen all the answers before, copied by students in classes before you. I don't like to see answers that look like they're just copied down (e.g. from the back of the book) -- makes me feel like I'm wasting my time grading them, and I'm pretty sure that students who do it aren't really learning anything. It's always wonderful to see some interesting attack on a problem by a student; I appreciate the struggle!)
- Keep up with the homework. Your fourth assignment is due today at midnight. Email with questions, or post to the discussion.
  Please save your work as a single pdf (lots easier for me to grade), and upload that to Canvas. Remember to keep the grader happy! You don't want a grumpy grader, trust me; they're not nearly as sympathetic!:)
- You have a new assignment, which will be due a week from Tuesday. That's because you have an exam coming up next weekend.
- End of next week is exam 1. More as we get closer, but section 2.1 is the last of the material to be covered on that exam. So you'll have five sections, 1.1-1.4 and 2.1, to study for the exam.
Today: we'll hit the highlights of Section 2.2: Induction
Links:
- Nothing new to report
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