Prove or Disprove: An odd integer minus an even integer is odd.
I am assuming you would define an odd integer and an even integer. than you would use quantifiers which shows your solution to be odd or even. I am unsure on how to show this…
[Math] An odd integer minus an even integer is odd.
elementary-number-theory
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Best Answer
An even number is an integer which is divisible by $2$. In other words, $n$ is if and only if $n=2m$ for some integer $m$.
An odd number is a number which is $1$ more (or less) than an even number. In other words, $n$ is odd if and only if $n=2m+1$ for some integer $m$.
So suppose $n$ is odd and $n$ is odd. Write $n=2m+1$ and $n'=2m'$.
What can you say about $n-n'$?