Discrete Math - 1.7.3 Proof by Contradiction

Exploring a method of proof known as contradiction where we assume p and not q, then work to show either if p then q or if not q then not p.

Video Chapters:
Introduction 0:00
What is Proof by Contradiction? 0:07
Proof by Contradiction with One Proposition 1:32
Contradiction Using an Implication 6:00
Up Next 9:29

Textbook: Rosen, Discrete Mathematics and Its Applications, 7e

[AA-ncxj]

While your videos have helped me get through some of this stuff, I just have to say I despise discrete math and I hope I never see it again after this class is over. Thank you for making it somewhat tolerable. <3

[adnanyeasir]

I have always hated proofs and it still hasn't changed

[gourav]

I dunno why but hearing her voice really makes me calm at the moments when discrete mathematics scaring the shit out of me

[hlby]

ma'am you are singlehandedly saving my grade in this class thank you!!!

[iseeawindow]

oh my god this is gold. youre about to save me for this upcoming midterm. THANK YOU

[ASHans-iler]

Thank you so much! You're incredibly clear. The step by step approach makes the method easy to follow.

[MosuaEkiosMOSUA]

After going through other videos on contradiction, I couldn't understand util I watch this vedio and it helps me on how to handle such questions on contradiction....

[kaujla]

For question 2, it's also true that if you add an odd number to an even number, then you'll get an odd number (correct me if I'm wrong). So could you have also taken this route?

1. 3n + n must be odd by addition of an odd integer
2. 3n + n = 4n
3. 4n = 2(2n)
4. 2(2n) = 2r where r = (2n) and r is an integer (dunno if the integer part is necessary)

OR even more directly done this:

1. 3n + 2 = 3(2k + 1) + 2 since we know n is odd, then
2. = 6k + 3 + 2
3. = 2 (3k + 2) + 1
4. = 2r + 2 where r = (3k + 2) and r is an integer, thus proving ¬q -> ¬p

Thanks! 😊

[nathnaeldereje]

You made my life easier!!, thank you so much

[rafiabdul]

This is so helpful. Thank you so much for these videos!!!

[halilibrahimkocak]

Hey, this videos about discrete mathematic published just before midterm. thank you for your support

[zhujune]

At 9:04, could you please explain more about " 3n-n must be odd by subtraction of an even and odd integer? "
Which theorem was used in this conduction?

[hammam]

helpful, Thanks so much
thumbs up, keep it going.

[ceejay]

In the final proof, if you could show that both sides are odd instead, would that also technically work?

[red-svqf]

At 4:26, what happened to the squares?

[DannyPhantumm]

Can someone criticize or verify my alternative proof for the last exercise?

Assume n is an integer, 3n+2 is even, and n is odd.
It follows 3n+2 = 2k, where k is an integer, by the definition of an even number.
3n + 2 = 2k -->
(2+1)n + 2 = 2k -->
2n + n + 2 = 2k -->
n = 2k - 2n - 2 -->
n = 2(k - n - 1)
which can be rewritten as n = 2r where r = k - n - 1, implying that n is even. This is a contradiction to our original assumption that n is odd. Therefore, when 3n+2 is even, then n is even. QED.

[claudioosorio]

Thanks for the videos. I'm sharing them with my classmates. Your content is great. We just need a bit of help from YT algorithm XD

[cringegabe]

i did not know that rational numbers are called rational numbers because of the ratio of a/b

[alifnm]

for the first one, why cant it have a common factor, cant rational numbers have common factors, e.g: 4/8

[saadshah]

why is everyone yapping about discrete being difficult when it is simply the easiest part of maths imo