Mat 300, Spring 2009
Final Exam, 05/12, 9:50-11:40, PSA 113
1. Operations and quantifiers
•Operations: conjunction, disjunction, biconditional, conditional.
•Propositional equivalence.
•Quantifiers: truth values, negations, and translations.
2. Methods of Proof
•Direct and indirect proofs of implication.
•Proof by contradiction. Irrationality of √2,√3.
•Proof of a biconditional.
•Proof by cases.
•Mathematical induction.
3. Sets
•Notation and the power set.
•Operations on sets.
•Generalized unions and intersections.
4. Inequalities
•Solving inequalities.
5. Functions
•Definition of a function.
•Injective, surjective, bijective functions.
•Composition of functions and the inverse of a function.
6. Denumerable and uncountable sets
•Proving that a set is denumerable using definition.
•Facts about denumerable sets. Showing that if A, B are denumer-
able then A∪Bis denumerable.
1
