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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 [tex] m [/tex] be [tex] 2x + 1 [/tex], and let [tex] n [/tex] be [tex] 2x [/tex].

Add [tex] m [/tex] and [tex] n [/tex] :

[tex] m + n [/tex]

[tex] (2x + 1) + 2x [/tex]

[tex] 4x + 1 [/tex]

Now substitute any value in [tex] x [/tex], since [tex] m + n [/tex] is [tex] 4x + 1 [/tex]

But by observation, [tex] 4x [/tex] is always EVEN.

AND any EVEN number plus ONE is always ODD.

THEREFORE, [tex] m+n [/tex] is odd is TRUE.

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