Description

INTRODUCTION TO LOGIC — Complete Study Guide (002)
A comprehensive, exam-ready resource covering everything from the meaning of logic to complex electrical network simplification — all in one clearly organized document.

📘 What’s Inside
1. Foundations of Logic

Origin of the term (Greek Logos) and its full definition

Real-life applications: law, computer science, mathematics, philosophy, and everyday decision-making

2. Statements (Propositions)

Clear definition: declarative, definite truth value, never both true and false

Extensive examples of statements — and non-statements (questions, commands, exclamations, variables)

Truth values (T/F or 1/0) and statement notation

3. Types of Statements

Simple vs. Compound statements — with fully worked examples

4. Negation (∼)

Definition, truth table, and multiple worked examples

5. Logical Connectives — Overview

Complete reference table: Negation, Conjunction, Disjunction, Implication, Biconditional

Symbol, reading, and usage for each

6. Conjunction (∧)

Truth table, truth condition, and 5 worked examples

7. Disjunction (∨)

Truth table, truth condition, and worked examples including compound evaluations

8. Conditional / Implication (→)

All reading forms (“if…then”, “implies”, “sufficient for”, “q if p”)

Hypothesis vs. conclusion, truth table, and worked examples

9. Biconditional (↔)

Definition, reading forms, truth table, and worked examples

10. Converse, Inverse & Contrapositive

Full definitions table and truth table for the contrapositive

Key insight: the contrapositive always has the same truth value as the original

Two fully worked examples breaking down all four forms

11. Logical Equivalence

Definition and test (tautology check)

Essential equivalences: Implication Law, Biconditional Law, De Morgan’s Law

12. Tautology & Contradiction

Definitions with examples of each

Fully worked truth-table proofs (Examples 2.22 & 2.23)

13. Laws of Algebra of Propositions

Complete 11-law reference table

Order of dominance (precedence) table

14. Truth Tables

Row-count formula (2ⁿ) with reference table

Three fully constructed truth tables, including tautology verification

15. Validity of Arguments

Structure: premises → conclusion

Validity test via tautology

Valid and invalid arguments fully worked with truth tables

Common valid argument forms: Modus Ponens, Modus Tollens, Disjunctive Syllogism, Hypothetical Syllogism, Constructive Dilemma

16. Electrical Networks ⭐

Switches as statements (closed = T, open = F)

Series (∧) and parallel (∨) connections with diagrams and truth tables

Complementary switches

Complex network simplification — from circuit diagram to simplified circuit, step by step

Drawing networks from logic expressions

17. Constructing Propositions from Truth Tables

Step-by-step method with a worked example

18. Duality Principle

Definition and the four conversion rules

19. Chapter Summary

Key concepts table, law formulas, and validity test summary

20. Additional Practice Questions

Multiple choice (with answers), truth table construction, simplification, validity testing, and network drawing/simplification

21. Quick Reference Card

All connectives, truth values, and key equivalences on one card

✅ Why This Guide Works
Every connective fully worked — definitions, truth tables, and multiple examples for each

Visual circuit diagrams — series, parallel, and complex networks drawn and simplified step by step

Exam-focused — common argument forms, validity testing, practice questions with answers, and a quick reference card

Complete coverage — from “what is a statement?” to simplifying complex electrical networks in a single document

MITIHANI POPOTE — Quality educational resources wherever you are.