Discrete Math - 1.7.2 Proof by Contraposition

Continuing our study of methods of proof, we focus on proof by contraposition, or proving the contrapositive in order to show the original implication is true.

Video Chapters:
Introduction 0:00
What is Proof By Contraposition? 0:07
Proof by Contraposition Practice 1 0:52
Proof by Contraposition Practice 2 3:50
Up Next 6:31

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

[joelhenningsen]

Very thankful for your videos! You give great examples and clearly show you steps. We all owe you one!

[nicholasshin]

Thank you so much. I am going to watch your videos this whole semester.

[vsufnyz]

Thank you so much for these series. Such a clear articulation of these concepts; so approachable. Cheers

[strawberrytofu]

In the first problem, if p was negated, wouldn’t that make n not an integer? Which conflicts with q because even numbers are integers.

[chiranjivishahi]

Helpful video and thank you so much for explaining in simple terms ❤kee p going on

[ganeshgump]

Im not sure if this is a dumb question but I was working on the last example problem and was wondering if my way of proving is correct. When you had the equation 3n+2 = 6k+5, could you subtract 2 from the left side to get 3n= 6k+3, divide the whole equation by 3 to get n=2k+1 to prove your proof? I'm not sure if I'm just thinking too algebraically or if my method of proving is a correct approach, so I'd appreciate help from anyone with more knowledge.

[Lyones]

Hi Kim. Thank you for all the videos. I had a question. How did 2( 3k +2) +1 get to 2r + 1, r = 3k +2 ... ? Where did the 'r' come from?

[Parth-ivgx]

Thank you. Your the reason i got a good grade in my class

[ケシ-mk]

does the meaning of proving ~q>~p is true equals to proving that ~q implies ~p is a tautology and by the use of equivalent statement of p>q and ~q>~p, p>q is a tautology, too? im so confused with this section and the previous.

[jeehill]

This makes 10x more sense than my text book (I dont get any kind of lecture in this class) and I still feel like I am trying to learn greek...

[azhua]

I dont understand the math 5:25, how're you allowed to arrange it like that?

[pintblAnkwaziT]

Hi. I understand the method in the video, but how would you decide what prood to use? If the examples were listed in the textbook homework section, would it matter what method of proof I used - so long as I proved it?

[MrMiracleteen]

Alright. I was with you the whole way. Then at 5:35. you decide to pull some math magic. 6k + 3 + 2 -> 2(3k + 2) +1 . Nah. How the heck do you put the 1 on the outside there. I'm gonna need some laws or something to back that up. Because How can you just stick the remainder on the outside.

[chhangsrengp]

Hello, I have a question. Do I need to learn Axioms before doing proof exercises?

while doing the exercise, I realized that I needed to be aware of some axioms to do the proof. Those Axioms can be found on page 926 in the textbook. I'm pretty sure that had I paid attention in high school, I would be quite familiar with those axioms, but since I wasn't always a good student in highschool.

So do you think that I need to read and learn those before I start doing proof exercises? How essential is it?

[papakwabena-cu]

how can you know that this method is applicable to your question