Prove the difference of any even integer minus any odd integer is odd.

permaneceerc 2020-12-31 Answered
Prove the difference of any even integer minus any odd integer is odd.
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Expert Answer

Caren
Answered 2021-01-01 Author has 96 answers

Consider the teorem, the difference of any even integer minus any odd integer is odd.
The proof is given as:
Let a=2q be an even integer by definition of even and
b=2r + 1 by definition of odd, where q and r are integers.
Consider, a  b=2q  (2r + 1)=2(q  r)  1=2m  1:
where m=q  r is an integer and
2m  1 is odd.
Conclusion:
The theorem < the difference of any even integer minus any odd integer is odd, is proved.

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