🧠 Introduction to Logical Reasoning

What is Logic?

  • Origin: Derived from Greek “logos” meaning “Thought” and “the word expressing thought”
  • Definition: Science of thought as expressed in language
  • Key Principle: Solve questions based on given information without concern for formal validity or truth
  • Core Concept: Conclusion must follow directly from given statements
  • Application: Used in reasoning, argument analysis, and decision-making

🌟 Key Insight: In logical problems, we don’t question whether statements are true in reality. We only determine what must be true IF the given statements are true!

🔍 Understanding Syllogisms

What is a Syllogism?

A syllogism is a deductive argument where a conclusion is drawn from two or more propositions called premises.

Structure of Argument:

  1. Premises: Given statements (usually 2-3)
  2. Conclusion: What must follow from the premises
  3. Assumption: All premises are considered true
Set A
Set B
A ∩ B

📊 Statement Forms & Categories

Four Basic Statement Forms

Statement Form Quantity Quality Symbol Example
All A are B Universal Positive A ⊂ B All dogs are animals
No A are B Universal Negative A ∩ B = ∅ No cats are dogs
Some A are B Particular Positive A ∩ B ≠ ∅ Some birds can fly
Some A are not B Particular Negative A – B ≠ ∅ Some fruits are not apples

Key Concepts to Remember

  • “Some” means: At least one (could be all)
  • “All” means: Every single one without exception
  • “No” means: Zero, none, not a single one
  • Particular statements: Don’t give information about all members
  • Universal statements: Apply to entire category

💪 Practice Exercises

Type I: Positive Conclusions

Example 1: Statements: Some kings are queens. All queens are beautiful.
A All kings are beautiful
B All queens are kings
C Both A and B
D Neither follows

Type II: Negative Conclusions

Example 2: Statements: No bat is ball. No ball is wicket.
A No bat is wicket
B All wickets are bats
C Both A and B
D Neither follows

🚀 Study Strategies

1

Master the Four Forms

Create flashcards for each statement type: Universal Positive, Universal Negative, Particular Positive, Particular Negative. Draw Venn diagrams for each.

2

Venn Diagram Approach

Always draw Venn diagrams for complex problems. Use different colors for different sets. Shade areas that are empty, mark areas that have at least one element.

3

Logical Rules Memorization

Memorize key rules: From “All A are B” you can conclude “Some A are B” but not vice versa. “No A are B” is equivalent to “No B are A”.

💡 Quick Memory Tips

Universal Statements

All A are B: Circle A completely inside Circle B.
No A are B: Two completely separate circles.

Particular Statements

Some A are B: Overlap the circles and put an ‘X’ in intersection.
Some A are not B: Put ‘X’ in A but outside B.

Conversion Rules

Convertible: “No A are B” ↔ “No B are A”
Not Convertible: “All A are B” → “Some B are A” only

Common Mistakes

• Don’t assume “some” means “some not”
• “All” doesn’t imply “only”
• “No” is absolute, not “few”