Proof by Contrapositive | Method & First Example

Learning objective: prove an implication by showing the contrapositive is true.

This video is part of a Discrete Math course taught at the University of Cincinnati.

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[فيصلحمد-حث]

3min video to explain a 2h lecture you are the GOAT!!!

[DonegalTweed]

Writing backwards that whole time was impressive... Also, great video it helped a lot!

[mohammedlaïdKachi]

Beautiful explaining ser, please continue with the same way and thank you so much

[youngdonlee]

My second comment of the day. You are awesome. You need to teach at a university level. You are an amazing source of help for my logic course.

[andrewharrison]

What a simple example. The direct proof really is walking through briars. Turning the problem round it is a stroll along the pavement.
Just beautiful at showing that contrapositives have real utility.

[trumanhung]

Prof Bazett you are awesome! Please come to teach in UofT.

[adambruneau]

These videos have helped so much, thank you! By chance is there any material for contrapositives that contain inequalities? for example : For every real number x, if 0 ≤ x ≤ 3, then 15 - 8x + x^2 > 0

[deborahanthony]

I love the way u teach ....keep uploading such videos ....it so helpful ....😊

[viveknayar]

Your videos are too good...Thank you for the help :)

[mtaur]

It is true - but harder to prove than one might expect - that if p (prime) divides ab, then p divides a or p divides b. The video is a fine way to go around this gap if needed.

[ReviewGame]

your backwards writing is better than my normal writing

[gabrielpadilla]

Dr. Trefor Bazett you are fucking awesome, thank you so much for sharing this content! It is very helpful

[maksfraszka]

that glass window really caught me by surprise

[todyprasetya]

can you please make proof by induction and proof by constructive dr? thank you in advance

[tvinforest]

Thank you first of all - but I really don't get it. I've made an example in order to explain what I don't get - tho I'm not sure if it's a valid one.
So let us assume that if P then Q. Then we can say if not Q then not P, right?
Now we will say that P is an even number and Q is a number such when it's multiplied by itself the result is a positive number.
We will use contrapositive - Then it means that if it's not Q then it's not P. Because not P is not an even number so it's odd.
But the square of an odd number is a positive number so it's Q. We now have if not Q then Q. How it's then Q and not Q at the same time?

[KingUnity]

How in the hell did you learn to write backwards like that

[TheGunzSkido]

why in my lecture note its written like this "Prove that for an integer n, if n^2 is odd, then n is odd. " .then the example is written like this "Use proof by contraposition. Assume n is even (i.e., not odd). Therefore, there exists an integer k such that n = 2k.
Hence,
n^2 = 4k^2 = 2 (2k^2) "

where did he get that 4k^2? or its the lecture note mistake?

[NIXRevolution]

you have to assume that n is an integer

[JohnCutter]

I wish my brain wasnt so literal. Regardless of the book or teacher once you write out the K stuff im thrown off. Although i get the logic from the start and the goal

[akshy]

Your channel has some problems. CONTACT YOUTUBE NOW. I can stream any of you videos after like 10s. It buffers forever then. How many views could've lost for you