STANDARD COMPETENCIES

 

 1. Create proofs using formal logic

 2. Demonstrate understanding of quantifiers

 3. Demonstrate understanding of set operations

 4. Prove propositions of set operations

 5. Demonstrate understanding of functions

 6. Prove propositions of functions, including propositions of one-to-one functions, onto functions, compositions of functions, and functions and sets

 7. Demonstrate understanding of relations

 8. Prove propositions of relations

 9. Demonstrate understanding of equivalence relations

 10. Prove propositions using mathematical induction

 

 

 TOPICAL OUTLINE

 

 I. Logic

     A. Truth tables

     B. Arguments and Tautologies

     C. Technique of proofs: direct proofs, contrapositive proofs, proofs by contradiction

     D. Quantifiers

 II. Sets

     A. Operations of sets

     B. Proofs of operations of sets

     C. Description of sets

 III. Functions

     A. Definition and examples of functions

     B. Functions and sets

     C. Proofs of functions and sets

     D. One to one functions

     E. Onto functions

     F. Composition of functions

     G. Characterization of one-to-one and onto functions in terms of sets

 IV. Relations

     A. Definition and examples of relations

     B. Reflexive, Symmetric, Transitive, and Antisymmetric relations

     C. Equivalence relations

     D. Proofs of relations and their properties

 V. Proofs of propositions that use mathematical induction