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Solved Propositional Logic Exercises

A comprehensive collection of solved exercises covering the core methods and techniques of formal logic.

This section features step-by-step solutions for propositional logic, predicate logic, and set theory problems. Exercises are organized by topic and difficulty level, supporting progressive mastery of formal proof techniques.

Problems and puzzles

Logic puzzles and mathematical problems
Logical reasoning challenges and real-world applications of formal techniques.

Truth tables

Truth table exercises with solutions
Constructing truth tables, identifying tautologies, contradictions, and contingencies. Full and abbreviated methods.

Set theory

Set theory exercises with solutions
Set operations, Venn diagrams, De Morgan's laws, expression simplification, relations, and functions.

Natural deduction

Natural deduction exercises with solutions
Formal proofs using the Gentzen system for propositional and predicate logic. Primitive and derived rules.

Formalization

Translating natural language into formal logic
Converting English sentences into the formal language of propositional and predicate logic.

More exercises by topic

• Validity and logical consequence
• Rules of inference
• Natural deduction — Overview
• Natural deduction — Primitive rules (propositional)
• Natural deduction — Derived rules (propositional)
• Natural deduction — Primitive rules (predicate)
• Natural deduction — Derived rules (predicate)
• Natural deduction with identity

Set theory — Additional topics

• Set operations using Venn diagrams
• Set simplification — De Morgan's laws and properties
• Intension and extension of sets
• Set cardinality