Proof: n is Odd if and only if 3n+5 is Even

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We prove n is odd if and only if 3n+5 is even using a direct proof and a contrapositive proof. This is, of course, a biconditional proof, which gives us two directions to handle!

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Z is integers numbers, it can be + or -, so n should be in N set?

yassineagguinechannel_

Thank you i am useful for university assignment 😊

ashannevishka

That's was very pretty explanation, but I'm having difficulties in dealing with this problem now
For every integer X, X + 4 is odd if and only if X + 7 is even, may you help please please

RasheedHamisi-gwbk

Do you have any tips on when the implication is less direct? Like say 5n-3 is odd -> n+4 is even. How would you go about proving the implication when there are constants added in?

sethfreitag

Thank you. For me, it was a 'eureka' moment when you decomposed 5 into 2(2) + 1. That part didn't occur to me, and it was like music :D

gord

A different approach for the 2nd:
3n+5 even
3n+3+2 is even
3n+3 is even
3(n+1) is even, 3 is odd then n+1 should be even, so n is odd

inmathswetrust

Thanks so much!!
I have learnt a lot!

aashsyed

Well explained 🙏We appreciate you Sir for the effort you put to share with us such knowledge, we really appreciate you sir

sfundoydube

what about something like n is even therefore 2n+3 is odd

basedland

hey sean how are you... sean can you make a video on how to make/find a class limit in a frequency table. As, you know your content is the swankiest content on the internet...!!!

arishkhan

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