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.
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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 ![4x + 1 4x + 1](https://tex.z-dn.net/?f=%204x%20%2B%201%20)
But by observation,
is always EVEN.
AND any EVEN number plus ONE is always ODD.
THEREFORE,
is odd is TRUE.