## Sections covered and to be covered in class

Covered

• Section 1.1: Statements and compound statements;
• Section 1.2: Negation of Statements;
• Section 1.3: Making and using truth tables;
• Section 1.4: Converse and contrapositive;
• Section 1.5: Logical equivalence;
• Section 1.6: Necessity and sufficiency;
• Section 1.7: The laws of logic;
• Section 1.8: Disjuctive normal form: using "only", "or", and "not";
• Section 1.9: Logical implication;
• Section 1.10: Arguments: rules of inference;
• Section 2.1: Open statements;
• Section 2.2: Quantifiers;
• Section 2.3: Negating a quantified statement;
• Section 2.4: The division algorithm;
• Section 2.5: Some examples of written proofs;
• Section 2.6: Divisibility;
• Section 2.7: Prime numbers;
• Section 3.1: Introduction to Principle of Mathematical Induction;
• Section 3.2: Principle of Mathematical Induction (PMI);
• Section 3.3: Examples;
• Section 3.4: Variants of PMI;
• Section 3.5: Strong Form of Induction;
• Section 3.6: More Examples;
• Section 3.7: Recursive Definitions;
• Section 3.8: Recursion and PMI;
• Section 3.9: Examples involving Divisibility;
• Section 4.1: What is a set;
• Section 4.2: The empty set;
• Section 4.3: Subsets;
• Section 4.4: Proper subsets;
• Section 4.5: The power set;
• Section 4.6: Set operations;
• Section 4.7: Venn diagrams;
• Section 4.8: Counting sets and subsets;
• Section 5.1: Base b representations;
• Section 5.2: The number of digits;
• Section 5.3: Unique factorization and its consequences;
• Section 5.4: The greatest common divisor and the least common multiple;
• Section 5.5: The Euclidean algorithm;
• Section 5.6: Relatively prime integers;
• Section 5.7: Arithmetic (mod m);
• Section 5.8: Testing for divisibility;
• Section 6.1: Cartesian Products;
• Section 6.2: Functions;
• Section 6.3: One-to-one and onto functions;
• Section 6.4: Equality of functions;
• Section 6.5: Function compositions;
• Section 6.6: The identity functions;
• Section 6.7: Inverse functions;
• Section 6.8: The floor function and the ceiling functions;
• Section 6.9: Relations;
• Section 6.10: Properties of relations;
• Section 6.11: Equivalence relations;
• Section 7.??: Cardinality of sets.
To Be Covered