Discrete Math Proof: Proving Equivalence of 4 Statements

AI Thread Summary
The discussion revolves around proving the equivalence of four statements related to the parity of n and n². A participant expresses confusion about the problem, noting that two statements appear to contradict each other regarding odd and even classifications. Miscommunication arises over the correct transcription of the statements, particularly with statement (c), which is identified as a typo. Participants clarify that the proof can proceed by correcting the typo to n³ being odd instead of n². The conversation emphasizes the importance of accurate problem transcription in mathematical proofs.
MarcL
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Homework Statement


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.

Homework Equations



None really, just the use of different proofs ( indirect, etc...)

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?
 
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MarcL said:
(a) n2 is odd.
(b) 1 − n is even.
(c) n2 is odd.
(d) n2 + 1 is even.
Uh ... are you sure you copied (a) and (c) correctly?
 
I promise you I did, if you want to see the assignment yourself you can check :P --> #4 http://users.encs.concordia.ca/~grahne/comp232/assgn2.pdf
 
MarcL said:
I promise you I did, if you want to see the assignment yourself you can check :P --> #4 http://users.encs.concordia.ca/~grahne/comp232/assgn2.pdf
Exactly. You copied it incorrectly, as is obvious.
 
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.
 
MarcL said:
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.
You misunderstand. You copied the problem incorrectly. Do you not see the obvious mistake?
 
I somehow read d... definitely sorry about that. I'll go crawl in a hole now.
 
" 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.
 

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