9th Class Math Notes Chapter 8: Logic – Full Easy Notes, Statements, Truth Tables & Board Exam Tricks (Punjab Board 2025–2026)
Salaam dosto! Chapter 8 Logic padhte waqt bohot students sochte hain “Yeh maths mein logic kya kar raha hai?” lekin yakeen karo — yeh chapter bohot interesting aur scoring hai agar statements aur truth tables samajh lo 😎
Logic basically sahi-galat ka science hai — hum statements ko true ya false check karte hain using connectives (and, or, not, implies, etc.). Yeh chapter computer science, programming aur reasoning ke liye base banata hai.
Punjab board exams mein is chapter se 8–12 marks aate hain — truth tables, tautology, contradiction, logical equivalence aur conditional statements sab important hain. Thora practice kar lo toh paper mein full confidence rahega!
Quick exam tips for 9th class:
- Truth tables banana seekh lo — 3–5 marks ka question har saal aata hai
- Tautology (hamesha true), contradiction (hamesha false), contingency (kabhi true kabhi false) pe focus karo
- Logical connectives (∧ and, ∨ or, ¬ not, → implies, ↔ biconditional) ke symbols yaad rakho
- Common galti: Implication (p → q) ko galat samajhna — sirf jab p true aur q false ho tab false hota hai
Basic Logical Statements & Connectives
Statement ek sentence hai jo true ya false ho sakti hai (jaise “2 + 2 = 4” true hai).
Main Connectives
- Conjunction (AND, ∧): Dono true hon tab true
- Disjunction (OR, ∨): Kam se kam ek true ho tab true
- Negation (NOT, ¬): True ko false, false ko true
- Implication (IF…THEN, →): p → q false sirf jab p true aur q false ho
- Biconditional (IF AND ONLY IF, ↔): Dono same hon tab true
Truth Table Examples
Truth table har combination check karta hai (2^n rows jahan n = variables).
Example: p ∧ q
| p | q | p ∧ q |
|---|---|---|
| T | T | T |
| T | F | F |
| F | T | F |
| F | F | F |
Tautology, Contradiction & Contingency
- Tautology: Hamesha true (jaise p ∨ ¬p)
- Contradiction: Hamesha false (jaise p ∧ ¬p)
- Contingency: Kabhi true, kabhi false (jaise p → q)
Example: Prove p → p is tautology
Truth table mein har case mein true aata hai → tautology
Solved Examples – Board Style
Example 1: Construct truth table for (p ∧ q) → r
8 rows banayen (2³ combinations). Last column check karo — contingency hai (kabhi T kabhi F)
Example 2: Check if (p → q) ↔ (¬q → ¬p) is tautology
Truth table banao — dono taraf same values aayengi → tautology (logical equivalence)
Top MCQs Jo Har Saal Repeat Hote Hain
1. p ∧ ¬p kya hota hai?
Answer: Contradiction
2. Implication p → q kab false hota hai?
Answer: Jab p true aur q false ho
3. Tautology ka truth table mein last column kya hota hai?
Answer: Hamesha True
Important Short & Long Questions
- Define statement aur compound statement with examples. (3 marks)
- Construct truth table for (p ∨ q) ∧ ¬r. (4 marks)
- Prove that p → (q ∧ r) ≡ (p → q) ∧ (p → r). (5 marks)
- Show that (p → q) ↔ (¬q → ¬p) is a tautology using truth table. (5 marks)
- Differentiate between tautology, contradiction aur contingency with examples. (4 marks)
Logic Mein Confusion Hai?
Koi masla nahi — hamare tutors live session mein truth tables aur logical equivalences ko 15 minute mein crystal clear kar dete hain. Free demo le lo WhatsApp pe! Free Demo Book Karo
Roz truth tables banao aur connectives practice karo — yeh chapter clear hone ke baad programming aur reasoning mein bohot madad milegi.
Allah hafiz aur best of luck for 9th board exams 2026! 🌟
