# FA18:Prelim 1 guide

From CS2800 wiki

Prelim 1 will cover material all material covered in lecture and the homework up to and including material covered on Wednesday 9/19. Material that you've had homework problems on will be stressed more heavily. The exam will be closed book, closed notes, and will be 90 minutes long.

File:Fa18-prelim1-sample.pdf are some questions from past prelims. These questions are 10-15 minute questions; I would expect 4-7 of them on an exam. (File:Fa18-prelim1-sample-sol.pdf)

Here is a brief summary of what we've covered; for an exhaustive list see the Main Page.

- Proof techniques
- be able to write good proofs. Know how to use and prove various kinds of propositions
- Be able to do the proofs we've done in lecture or on the homework (here is a list of all claims on the wiki)
- Be able to find the logical negation of a proposition
- Be able to write proof by contradiction.
- Understand diagonalization proofs.

- Know and be able to apply definitions (both formal and informal):
- Set definitions: union, intersection, power set, cartesian product, empty set, .
- Functions: function, partial function, left inverse, right inverse, two-sided inverse, injectivity, surjectivity, and bijectivity , , , countable
- Relations: relation, reflexive, symmetric, transitive, equivalence relation, equivalence class, A/R, well-defined functions from A/R. (Note: these will be covered Monday and Wednesday in lecture).

- Know and be able to apply basic results
- Relationship between 'jectivity and inverses
- Countability or uncountability of .