Math Help - Question about a few explanations i do not understand.

1. Question about a few explanations i do not understand.

since 3n+2 is even so is 3n
how is 3n even?? and how is 3n+2 even?

if we add subtract an odd number from an even number ,we get an odd number so 3n - 2 = 2n is odd??? i don't get this at all

then it follows that but this is obviously not true, there fore our supposition was wrong, and the proof by contradiction is complete.

i'm so lost i don;t understand what is being said and it is getting really frustrating please help me understand this in English.

2. Originally Posted by camboguy
since 3n+2 is even so is 3n
how is 3n even?? and how is 3n+2 even?
Well for all $n \in \mathbb{Z}$ this is not true. Consider $n = 1 \implies 3\times 1+2 = 5$

But if $n$ itself is even then this could be true, do you have any other information?

the question is asking me to prove that if n is an integer and 3n+2 is even, then n is even using contradiction.

i just posted another thread about how i don't understand what contradiction is and iv been trying a few days now to understand what it is and wanted to do it on my own but its just breaking me down and i just don't understand what contradiction is.

4. In a proof by contridiction you take the orignal claim $3n+2$ is even and negate it. Then show that leads to a contridiction. You can then imply the opposite is true.

Here's some examples Proof by contradiction - Wikipedia, the free encyclopedia

In this particular proof for $\forall n \in \mathbb{Z}, 3n+2$ is even given $n$ is even you just need to use some simple logic.

You are told $n$ is even so start with $n=2k, k \in \mathbb{Z}$ , now $3n+2 = 3(2k)+2 = 6k+2 = 2(3k+1)$ and you are finished.