Example 2 - Chapter 9 Class 9 - Propositions and their Converses (Ganita Manjari)

Transcript

Example 2 Proposition P: If a number is a multiple of 6, then it is a multiple of 3. Converse Q: If a number is a multiple of 3, then it is a multiple of 6. Check if statements P & Q are true Let’s check if both statements are true or not Checking if Proposition P is true P: If a number is a multiple of 6, then it is a multiple of 3. Lets n be the number which is a multiple of 6 𝑛=6𝑘 𝒏=𝟑 × 𝟐𝒌 Thus, 𝑛 is a multiple of 3 Thus, Proposition P is true Checking if Converse Q is true Q: If a number is a multiple of 3, then it is a multiple of 6 This is false Example: 9 is a multiple of 3 but not of 6. Thus, Converse Q is false