Notice that my office hours are now posted on my main page.

Watch this space. I will supply a list of proofs which students can present -- they will be assigned to pairs of students or individual students on a first-come first-served basis. The assignment involves preparing a slide presentation of the proof of the theorem you are assigned (you can run these past me before presenting them -- I do not want to critique proof presentations which are incorrect, as I am interested in communication more than in testing of specific content). The presenters should each take a role in the actual presentation, and should both be expected to answer questions from the audience or from me.

I remind you that presentations may run into the final exam period. If they do, not only presenters but the entire class will be expected to appear. Attendance will be taken if this happens.

I am hoping that we will have one more lab day where we can complete all lab work that is still dangling. If you have handed in the first logic lab and/or the LaTeX assignment you should expect to get an email about it. I am still accepting those assignments.

On Monday remember that we are working on the constant multiple property of limits, and also I may do something to encourage people to continue computer lab activities.

These are proofs to be written in mathematical English. You are welcome to structure them with goal statements, indentation, line numbers, and so forth as I do in class. You are also welcome to write plain paragraphs of English, as long as they contain what is needed to communicate the proof. Try to be explicit about where you are using or proving quantified statements, as I was in my board examples. Other logical issues also arise in some of these problems.

4.1, 4.2, 4.5, 5.10 (define largest element of a set in your work), 5.26, 5.46

Having constructed this assignment, I comment that the book does not give me perfect material for what I have in mind. These are interesting proof problems, but not really a systematic quantifier reasoning workout. Please work on them and ask questions about them if you need to...

I am thinking of posting notes on the examples I did in class Wednesday. If I do, they will appear here.

Section 2.10 problems: 2.68, 2.70, 2.71, 2.72, 2.75, 2.76, 2.78, 2.79

Here are the solutions. They are not completely typeset yet; I will update them fully later.

On Sept. 30th, I am hoping to have **a computer lab** on propositional logic. It might be on the 5th, depending on issues I may encounter in setting it up.

On Wednesday Oct. 7 we will have **Test I**, covering material we will have done up to the Sept 28th lecture; I changed my mind and am leaving
Oct. 5 free for review or other activities. The coverage of the test is still up to the topics covered on Sept. 28th.

3.5, 3.6, 3.7, 3.8, 3.9, 3.10

It's quite brief and I **know** that Dr. Kaiser covered a couple of these. What I hope to see on these papers
is a nice clear writeup (this class is about communication!). I'll talk more about the kind of style I want to see in
my lecture on Monday.

Prove the following using the rules in the style manual, and **not** using any kind of replacement of statements with other statements of logically
equivalent form (for example, do not use de Morgan's laws).

- Prove
`~(P v Q) <-> ~P & ~Q`(Notice that this is the one of de Morgan's laws that is not proved as an example). - Prove
`(P v ~Q) & (Q v R) -> P v R`(Hint: this is a proof by cases) - Prove
`(P -> Q) <-> (~Q -> ~P)`(the well known equivalence of an implication with its contrapositive; we did this in class, so it is low effort if you have perfect notes, but you might do better to work it out yourself. Do not use the rule of modus tollens or the alternative strategy for proving an implication; this makes it too easy) - Verify the rule of
**destructive dilemma**(you have the verification of constructive dilemma in class and in the style manual as a model). The rule says that if P implies R, and Q implies S, and either R is false or S is false, then either P or Q must be false. Start, of course, by expressing the premises and the conclusion in symbols.**This part had a typo in it -- two letters were exchanged**

I use `->` for implies, `~` for not and `&` for and here because they are on my keyboard...

Prove the statement `((A -> B) & (B -> C)) -> (A -> C)` using the rules described in the style manual. This justifies the well-known logical rule "hypothetical syllogism".

Prove the statement ` (P -> Q) <-> ~(P & ~Q) ` using the rules described in the style manual. This verifies a perhaps unexpected logical equivalent of implication.

Exercises 2.1, 2.2, 2.9, 2.10, 2.13. 2.14, 2.15, 2.16, 2.20, 2.25, 2.27, 2.31, 2.34, 2.39, 2.47, 2.48, 2.49

I do expect to hear some questions on Wednesday!

Exercises 1.3, 1.4, 1.5, 1.6, 1.10 (these are different examples for each part), 1.11, 1.14, 1.19, 1.21, 1.22 (I was writing A^{c} in lecture for what they write as A: that is, the complement of A or U-A), 1.28, 1.30, 1.32, 1.33, 1.35.

Every now and then a homework problem may turn into a class example, particularly as I am likely to mark only selected problems from each set; be ready on Monday with your questions about these!

It would be a good idea to read sections 1.1-1.3 in preparation for Wednesday's lecture.

The first homework assignment will be posted Wednesday after the lecture.