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Rajan@2021
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Show that every possible integer is either even or odd.

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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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  1. 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

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