What's the best way to master Tautology and Contradiction quickly?

Master Tautology and Contradiction by understanding the core concepts first, practicing regularly with our worksheets, and applying the shortcut techniques provided.

Tautology and Contradiction

Tautology and Contradiction problems involve identifying statements that are always true (tautologies) or always false (contradictions) regardless of the truth values of their component propositions. Examples include p ∨ ¬p (tautology) and p ∧ ¬p (contradiction).

10Worksheets

200+Practice Questions

MediumDifficulty

2-3 hoursHours to Master

What You'll Learn

Introduction & Overview Why This Matters How to Solve Pro Tips & Tricks

Shortcut Methods Common Mistakes Practice Worksheets Exam Importance

Introduction to Tautology and Contradiction

Prerequisites

Truth table construction Basic connectives Logical necessity concept Contradiction detection

Why This Matters: Tautology/Contradiction problems appear in 1-2 questions in SSC CGL and Banking PO exams. They test understanding of logical necessity and impossibility.

How to Solve Tautology and Contradiction Problems

Step 1: Construct a truth table for the given expression

Step 2: Examine the output column for all input combinations

Step 3: If all outputs are True → Tautology

Step 4: If all outputs are False → Contradiction

Step 5: If outputs are mixed → Contingent (neither)

Step 6: For simple expressions, use known logical laws

Step 7: Present the classification

Pro Strategy: A tautology is true in every possible scenario. A contradiction is false in every possible scenario. Use truth tables for definitive classification.

Example Problem

Example: Is p ∨ ¬p a tautology, contradiction, or contingent? Solution: Step 1: Truth table: p=T → ¬p=F → T∨F=T; p=F → ¬p=T → F∨T=T Step 2: All outputs are True Step 3: Therefore, p ∨ ¬p is a tautology Answer: Tautology

Pro Tips & Tricks

p ∨ ¬p: Law of Excluded Middle (tautology)
p ∧ ¬p: Law of Non-Contradiction (contradiction)
p → p is a tautology (self-implication)
p ↔ p is a tautology (self-biconditional)
Any expression that is always true regardless of inputs is a tautology
Any expression that is always false regardless of inputs is a contradiction

Shortcut Methods to Solve Faster

If an expression can be simplified to p ∨ ¬p, it's a tautology

If an expression can be simplified to p ∧ ¬p, it's a contradiction

p → p ≡ T (tautology)

p ↔ ¬p ≡ F (contradiction)

A tautology's negation is a contradiction

Common Mistakes to Avoid

Classifying a contingent statement as tautology or contradiction

Forgetting to check all input combinations

Assuming an expression is tautology without verification

Confusing tautology with logical equivalence

Practice Worksheets

Practice makes perfect! Work through these worksheets to master Tautology and Contradiction. Each worksheet contains 20 questions with detailed explanations. Start from Worksheet 1 and progress through increasing difficulty levels.

Worksheet 1 Beginner Beginner level - Perfect for building foundational understanding

Worksheet 2 Beginner Beginner level - Perfect for building foundational understanding

Worksheet 3 Beginner Beginner level - Perfect for building foundational understanding

Worksheet 4 Intermediate Intermediate level - Test your understanding with moderate difficulty

Worksheet 5 Intermediate Intermediate level - Test your understanding with moderate difficulty

Worksheet 6 Intermediate Intermediate level - Test your understanding with moderate difficulty

Worksheet 7 Advanced Advanced level - Challenge yourself with complex problems

Worksheet 8 Advanced Advanced level - Challenge yourself with complex problems

Worksheet 9 Advanced Advanced level - Challenge yourself with complex problems

Worksheet 10 Advanced Advanced level - Challenge yourself with complex problems