A Course in Discrete Math/Chapter 1 Logic

Section 1: Propositional Logic

Schedule

1. Read the subsections on propositions, negation, conjunction, disjunction, and truth tables.
2. Video 0000: Introduction
3. Video 0001: Propositions
4. Video 0002: Negation
5. Video 0003: Conjunction and disjunction
6. Video 0004: Conditionals
7. Read the subsections on complex truth tables and bit-wise operations.
8. Video 0005: Propositional variables and complex truth tables
9. Video 0006: Precedence and bit-wise operations.
10. Homework set 1
11. Video 0007: Homework set 1

Notes

At the end of this section, you should know:

• Definitions
  • Proposition
  • Truth value: True and false
  • Propositional operators: Negation, conjunction, disjunction, conditional, biconditional.
  • Propositional variable
  • Truth table
• Notation
  • $\neg ,\land ,\lor ,\oplus ,\to ,\leftrightarrow$
  • $\bigwedge _{i=1}^{n}p_{i}$ and $\bigvee _{i=1}^{n}p_{i}$.

Know how to identify propositions.

Know how to translate from an English sentence to a symbolic proposition, and vice versa.

Know how to construct an arbitrary proposition's truth table.

Know the precedence rules for operators.

Section 2: Propositional Equivalence and Satisfiability

1. Read the subsections on propositional equivalences and De Morgan's laws.
2. Video 0008: Propositional Equivalence