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I taught propositional logic a few weeks ago using Discrete Mathematics: An Open Introduction, 3rd edition. See chapter 1 and 3.1.

The topics includes

  • logical connectives
  • implications
  • converse and contrapositive
  • universal and existential predicate
  • truth table
  • valid logic argument

The students found the exercises in the book a little bit too easy for them. So I gave some Knight-and-Knaves type logic puzzles. Then students ask what does this has to do with what they learned in class.

I wonder how can I give some logic problems, which are hard, but not like puzzles.

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Here are all of the textbook chapters and assignments related to logic which I wrote for my Discrete Mathematics course last semester. We spent about half of the course time (8 weeks) on this content.

It contains a full treatment of the connectives and quantifiers, and includes problems from a "boolean calculus" perspective, from a "natural deduction" perspective, and interweaves connections to real mathematical usages by using and proving theorems about equalities, inequalities, parity statements, and divisibility statements.

All of these are still fairly rough and incomplete (especially chapter 4 of the textbook).

https://drive.google.com/drive/folders/19pXwLTowCwz1frNnVFNk0_v7KknxqXyJ?usp=sharing

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You might want to consider mining Ramsey Theory for that purpose. In particular, the theorem on friends and strangers has a proof with beautiful logic. (For that matter, so does Euler’s proof of the necessity of the form of even perfect numbers.)

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