Class 9 Maths | Ganita Manjari Part 2 | Ex 9.1 Q14 | Counterexamples | Proportions and Converses

📘 Class 9 Maths | Ganita Manjari Part 2 | Chapter 9 | Exercise 9.1 Question 14 In this video, we solve Question 14 of Exercise 9.1 – Propositions and their Converses from Class 9 Maths Ganita Manjari Part 2 with an easy, step-by-step explanation. Can a formula that gives prime numbers in many cases always produce a prime number? 🤔 In this question, we find counterexamples to two statements involving powers of 2 and learn how to prove that a mathematical claim is false. 📚 Question 14: Find counterexamples to the following statements. (i) If n is a prime number, then 2ⁿ − 1 is a prime number. (ii) If n is an even number, then 2ⁿ + 1 is a prime number. ✅ Counterexamples explained: 🔹 (i) Take n = 11, which is prime. 2¹¹ − 1 = 2047 = 23 × 89. Therefore, 2047 is not prime. 🔹 (ii) Take n = 6, which is even. 2⁶ + 1 = 65 = 5 × 13. Therefore, 65 is not prime. 🎯 What you will learn: How to find counterexamples in mathematics Prime numbers and composite numbers How to disprove a mathematical statement Propositions and logical reasoning Class 9 Maths Exercise 9.1 Question 14 This video is useful for Class 9 students studying Ganita Manjari Part 2 and preparing for school mathematics examinations. 👍 Like the video if it helps you understand the concept. 📢 Share it with your classmates. 🔔 Subscribe for more Class 9 Maths solutions. 💬 Challenge: Can you find another value of n that makes either statement false? Share your answer in the comments! #Class9Maths #GanitaManjari #Exercise91 #Counterexamples #PrimeNumbers