Show that every positive integer is …
CBSE, JEE, NEET, CUET
Question Bank, Mock Tests, Exam Papers
NCERT Solutions, Sample Papers, Notes, Videos
Posted by Sonali Verma Myira Soni 4 years, 4 months ago
- 2 answers
Related Questions
Posted by Ananya Sv 1 year, 3 months ago
- 1 answers
Posted by Gurleen Kaur 1 year, 3 months ago
- 0 answers
Posted by Ashish Chaudhary 1 year, 3 months ago
- 1 answers
Posted by Manoj Thakur 1 year, 3 months ago
- 0 answers
Posted by Sabin Sultana 1 year, 3 months ago
- 0 answers
Posted by Sethpoulou Apoulou 1 year, 3 months ago
- 0 answers
Posted by Sana Dharwad 1 year, 3 months ago
- 0 answers
Posted by Nitin Kumar 1 year, 2 months ago
- 1 answers
myCBSEguide
Trusted by 1 Crore+ Students
Test Generator
Create papers online. It's FREE.
CUET Mock Tests
75,000+ questions to practice only on myCBSEguide app
Preeti Dabral 4 years, 4 months ago
According to the question, we have to show that every positive integer is either even or odd.
Let us assume that there exists a smallest positive integer that is neither odd nor even, say n. Since n is the least positive integer which is neither even nor odd, n - 1 must be either odd or even.
Case 1: If n - 1 is even, n - 1 = 2k for some k.
But this implies n = 2k + 1
This implies n is odd.
Case 2: If n - 1 is odd, n - 1 = 2k + 1 for some k.
But this implies n = 2k + 2 = 2(k + 1)
This implies n is even.
Therefore,In both cases , we arrive at a contradiction.
Thus, every positive integer is either even or odd
0Thank You