# Homework Help: Discrete math proof

1. Feb 16, 2015

### MarcL

1. The problem statement, all variables and given/known data
Prove that the following four statements are equivalent:
(a) n2 is odd.
(b) 1 − n is even.
(c) n2 is odd.
(d) n2 + 1 is even.

2. Relevant equations

None really, just the use of different proofs ( indirect, etc...)
3. The attempt at a solution

I'm having trouble with this one because of (2) things. First, the question makes no sense ( unless I'm reading it wrong) because, as I understand it now, it is asking to prove all statements are equivalent BUT 2 of them are eve and the rest is odd. Secondly, I'm having trouble with it because of the definition that n=2k is EVEN and n=2k+1 is odd because I tried this:

Supposle n is odd.
n=2k therefore n=(2k)2= 22k2 = 2(2k2) which goes against the definition.

Can anyone point me in the right direction?

2. Feb 16, 2015

### phinds

Uh ... are you sure you copied (a) and (c) correctly?

3. Feb 16, 2015

### MarcL

4. Feb 16, 2015

### phinds

5. Feb 16, 2015

### MarcL

not at all, my assumption of n being even was just wrong, but that's all I've been taught before so I thought it was a set definition. anyway case closed.

6. Feb 16, 2015

### phinds

You misunderstand. You copied the problem incorrectly. Do you not see the obvious mistake?

7. Feb 16, 2015

### MarcL

I somehow read d... definitely sorry about that. I'll go crawl in a hole now.

8. Feb 19, 2015

### Merlin3189

" I'll go crawl in a hole now." Can't see any reason to do that! Just change c) to n3 is odd , then carry on. No need to worry about a trivial typo.

So, " n=2k therefore n=(2k)2 " what makes you say that?
It's just like saying n=n2 which is not generally true.