# Math Help - [SOLVED] Proving a theorem without using contradiction

1. ## [SOLVED] Proving a theorem without using contradiction

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2. Originally Posted by racewithferrari
The following theorem has the form of an implication.
If n is an integer and 3n+2 is even, then n is even.
Suppose that $3n+2=2k$ then $3n=2k-2$.
What does that tell you?

3. Originally Posted by racewithferrari
The following theorem has the form of an implication.

If n is an integer and 3n+2 is even, then n is even.

Give a direct proof of this theorem without using contradiction.
Since $3n+2$ is even we may state WLOG that $3n+2=2z\implies 3n=2(z-1)$ and since $2\nmid 3$ it must be true that $2\mid n$. The conclusion follows.