This is the basic and conceptual question from real numbers in which we have been asked to prove that every possible integer is either even or odd.
Kindly give me a detailed solution of this question
RS Aggarwal, Class 10, chapter 1A, question no 5
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Let I be a positive integer
We can now write I in the from of
I=pq+r
So, pq+r can either be even or odd.
Since, pq+r yields either even or odd number
⇒ if pq+r is even
pq+r=2x
and if odd
pq+r=2x+1
So, I=2x or 2x+1
⇒I=odd or even