For all integers m and n, if m is odd and n is even, then m+n is odd.
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For all integers m and n, if m is odd and n is even, then m+n is odd.
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ANSWER: TRUE
Let us prove it.
m is odd and n is even.
Let be , and let be .
Add and :
Now substitute any value in , since is
But by observation, is always EVEN.
AND any EVEN number plus ONE is always ODD.
THEREFORE, is odd is TRUE.