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

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!
Another proof by contrapositive: • Proof by Contrapositiv...
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[@ChocolateMilkCultLeader]

The subtracting 2n was slick

[@WrathofMath]

Agreed! It's weird, but it works!

[@gord01100]

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

[@yassineagguinechannel_1108]

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

[@sethfreitag279]

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?

[@gracefulpetals2]

so grateful you made this video

[@aashsyed1277]

Thanks so much!!
I have learnt a lot!

[@ashannevishka4495]

Thank you i am useful for university assignment 😊

[@RasheedHamisi-gw1bk]

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

[@sfundoy5dube59]

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

[@WrathofMath]

Thank you!

[@kanchansoni6693]

Good explanation sir

[@WrathofMath]

Thank you!

[@inmathswetrust5293]

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

[@WrathofMath]

Slick - I like it!

[@inmathswetrust5293]

@@WrathofMath thank you

[@mathsoldier3413]

The first direction is simple 👌🏽😂

[@arishkhan6786]

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...!!!

[@WrathofMath]

I'm great Arish - good to see you! Do you mean like a lesson talking about class widths, like you might do to make a histogram?

[@arishkhan6786]

@@WrathofMath exactly...and glad to hear that too

[@basedland]

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

[@WrathofMath]

Let me show you a similar example. Say n is even therefore 4n - 5 is odd. Then we have...
n = 2k
4n - 5 = 4(2k) - 5 = 8k - 5 = -2(-4k + 3) + 1. Hence, it is one more than a multiple of 2, and so is odd.

[@gemslk]

best video

[@WrathofMath]

Thank you!