Module 5. Disjunctions and Conjunctions

This module presents the rules for symbolizing disjunctions (‘or’ sentences) and conjunctions (‘and’ sentences), how to create truth tables for conjunctions and disjunctions, and the rules which apply to conjunctions and disjunctions. Topics studied in this module include:

1. Applying Formal Logic only to statements;
2. Symbolizing Simple Positive and Negative Claims;
3. The Laws of Non-Contradiction and Excluded Middle;
4. The Rules of Reiteration and Double Negation;
5. Introduction to Basic Truth Tables;
6. Introduction to Basic Venn Diagrams;
7. Making Sentences more Precise;
8. Making Sentences more Concise;
9. Distinguishing the Explicit, Literal Meaning of Logical Connectives from Implicatures;
10. Testing the Validity of Rules of Inference;
11. Making use of formal tools to reason more methodically;
12. Making use of formal tools to more objectively approach controversial topics.

• 5.1 Symbolizing Disjunctions and Conjunctions
  • 5.1.1 Disjunctive and Conjunctive Claims
    • Three Types of Claims
    •  Atomic Sentences (Simple Statements)
    • Negations (NOT)
    •  Disjunctions (OR)
    •  Conjunctions (AND)
  • 5.1.2 Symbolizing Disjunctions
    • Symbolizing Disjunctions
    • Multiple Disjunctions
    • Rephrasing More Literally
    • Unless
    • Negation
  • 5.1.3 Symbolizing Conjunctions
    • Symbolizing Conjunctions
    • Multiple Conjunctions
    • Conjunctions with Disjunctions
    • Conjunctions with Negations
  • 5.1.4 Symbolizing Neither-Nor and Not-Both
    • Neither Nor
    • Not Both
    • Review
  • Submodule 5.1 Quiz
• 5.2 Truth Tables for Conjunctions and Disjunctions
  • 5.2.1 Truth Tables for Disjunctions
    • The Truth Table for Disjunctions
    • Truth Tables with Disjunctions
  • 5.2.2 Truth Tables for Conjunctions
    • The Truth Table for Conjunctions
    • Truth Tables with Conjunctions
  • 5.2.3 Truth Tables for Complex Conjunctions and Disjunctions
    • More Complex Sentences
    • Creating a Truth Table with Three Atomic Sentences
  • 5.2.4 Truth Tables without Limits
    • Calculating Rows
    • Calculating Columns
    • Infinite Conjunctions and Disjunctions
  • Submodule 5.2 Quiz
• 5.3 Rules for Conjunctions and Disjunctions
  • 5.3.1 Conjunction Rules
    • Conjunction Elimination (&E)
    • Valid and Invalid Uses of &E
    • Conjunction Introduction (&I)
    • Valid and Invalid Uses of &I
  • 5.3.2 Disjunction Introduction
    • Disclaimer
    • Disjunction Introduction (vI)
    • Valid and Invalid uses of vI
  • 5.3.3 Distribution
    • Truth Functional Equivalence
    • The Rule of Distribution (DISTRIB)
  • 5.3.4 Disjunctive Syllogism
    • Disjunctive Syllogism (DS)
    • Truth Table for Disjunctive Syllogism
    • Valid and Invalid Uses of Disjunctive Syllogism
  • 5.3.5 Fallacies with Disjunctions
    • Affirming the Disjunct
    • False Dilemma and Alternative Advance
  • Submodule 5.3 Quiz
• 5.4 Practice with Conjunctions and Disjunctions
  • 5.4.1 Practice Translating Conjunctions and Disjunctions
  • 5.4.2 Practice Using Truth Tables with Conjunctions and Disjunctions
  • 5.4.3 Practice with DeMorgan’s Law (DEM)
    • DeMorgan’s Rule (DEM)
  • 5.4.4 Practice with Enthymemes for Conjunction and Disjunction
    • Enthymemes
  • Submodule 5.4 Quiz