Contrapositive of a Conditional Statement

The contrapositive of "p implies q" is "not q implies not p". It looks quite different, but in fact is logically equivalent to the original conditional, which means we can use them interchangeably.
Learning Objectives:
1) Identify the logical structure of the contrapositive to a conditional
2) Rewrite a sentence in it's contrapositive form
3) Use that the contrapositive is logically equivalent to a conditional
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This video was created by Dr. Trefor Bazett

[@vikranttyagiRN]

Though these videos are short but they are incredibly precise and up to the point. Great Stuff

[@skellingtonmeteoryballoon]

After this class, I was seeing p's and Q's in everything. Lol

[@MohamedElsayed-fv2kp]

The videos are short, but the value is incredible. Thank you so much .

[@cleverqwerty4504]

Have exams starting next week which have absolutely nothing to do with discrete math.... And here I am... hooked to this playlist...

[@DrTrefor]

Haha good study tactics imo;)

[@alterwinters5848]

Short Video not 10-20 mins and fast to learn in 4 mins tysm!

[@ShoaibAli-er4id]

You just solved my problem ,I was scratching my head whole day having problem in implications, contrapositive,double arrow...but all got easy for me...thank you sir

[@vaibhavshahi8244]

Your videos are damn good for clearing the concepts up to the point

[@Hooghog]

Great explanation, thank you! The following statements seemed to stick with me a bit more in case they're helpful for anyone: p = 'I study hard', q='I will pass' 1) p->q = 'If I study hard, then I will pass' (sucks if I study hard and then _don't_ pass, but I'm satisfied with the other cases) 2) ~q->~p = 'If I didn't pass, then I didn't study hard' (sucks if I didn't pass and I actually _did_ study hard, but I'm satisfied with the other cases) 3) q\/~p = 'Either I passed, or I didn't study hard' (sucks if I didn't pass and I actually _did_ study hard, but I'm satisfied with the other cases) 4) ~p\/q = 'Either I didn't study hard, or I passed' (sucks if I studied hard and then I _didn't_ pass, but I'm satisfied with the other cases) Regardless that statement (1) was said before the exam and statements (2-4) were said after, They are ALL routed in the belief of 'If I study hard enough, then I will pass'. They are therefore all logically equivalent

[@kylefranklin151]

This is the comment I was looking for, thanks. The time change thing was confusing me because common sense indicates there are more variables at play here when you look at the English translations of the math, because the English translations aren't perfect translations of the math. The English writing contains more information than the simple math formula, but this is supposed to be a simple exercise illustrating the point, so I guess I gotta just let it go. I think it's helpful to anyone like me looking in comments to note that the English and math statements are not perfect equivalents, because the English has more going on, but he gave us the English just so we could hold something familiar. I'm expecting as the course goes on we will learn to make more sophisticated math representations of complex concepts, specifically making a representation of time

[@djtygre]

Really helpful about the grammar issues (also overlooked), also the either / or way of saying it.

[@justinhansen1328]

Great job on the video, it helped out a bunch.

[@jaswanthtalada.]

he is a great explainer

[@MichaelFaradayStnine]

Keep it your response lecturer , you very well done ✅

[@elisam81j]

Gracias profesor. Dios lo bendiga.

[@bobtate8426]

Was it your intent to say that "~p v q" is the same as saying "EITHER ~p or q is true"? Doesn't the use of "either/or" imply that ~p and q can't both be true (xor)?

[@DrTrefor]

The symbol v here denotes the inclusive or, not the exclusive xor

[@bobtate8426]

@@DrTrefor Thank you. I was under the impression that "either/or" was used to denote "xor", but after looking a little deeper into it, it looks like there's some disagreement between sources on the meaning. I guess it doesn't really matter as long as the intent is clear. Thanks again, these videos are great!

[@ali-un-waliullah313]

Very nice explanation. Merçi.

[@minhthien1752]

Does ~p->~q equivalent to ~(p->q)? Using truth table I see what they are not equivalent, but I thought negation could be distributed?

[@Shaatha]

Thank you this was helpful

[@noxx8608]

My only question is you said it's wrong to output. If I pass, then I studied hard as that implies passing is contingent on studying hard, but you put if I don't pass, then I didn't study hard that's the same thing is it not?

[@insertnamehere2752]

Why does xp stay xp when taking the contrapositive of xq implies xp?

[@tatyana6856]

hello, im having trouble understanding the contrapostive section. is the contrapositive (>q --> >p)?

[@EpiCuber7]

If >X means not x, and p -> q is your original statement, then yes

[@shaikhah7861]

thank you so much doctor

[@DrTrefor]

Most welcome!

[@ironsfamily6]

Great videos! I tend to have trouble efficiently learning from a textbook so these are a great help as I prepare for today's quiz. Side not: Does his voice cadence remind anyone else of Veritasium (the beard helps too I'm sure, lol)

[@sushreesuchismita6003]

thanks sir..

[@humanrightsadvocate]

1. If n² is even then n is even. 2. Either n² is odd or n is even. 3. If n is odd then n² is odd. 4. Either n is even or n² is odd. Proving either of these sentences proves them all. Proving statement 3 is trivial. (2k+1)² = 4k² + 4k + 1 = 2(2k²+2k) + 1. But we can consider 2k²+2k = q. And we know q is some integer because of the Closure Properties of Addition and Multiplication over the set of integers. So, we know statement 3 is true. Let's check. Statement 1. n² = 2, then n is even. Wait! Where did I go wrong?

[@VndNvwYvvSvv]

You cannot assume q is an integer.

[@ruweydhaajiofficial8552]

Thanks

[@lanzibangli1259]

New meaning to "stay on your Ps and Qs"

[@VndNvwYvvSvv]

It's "mind your Ps and Qs" meaning don't spill your pints and quarts of beer.

[@tannudadhich]

He isn't only teaching Math, he's also teaching English grammer 😊😊😊😊 and Best thing about this tutorial is videos is short and on point. I have better example: If I watch this Tutorial, then I'll pass. P ⇒ Q Either I didn't watch this tutorial, or I pass. ~ P ∨ Q If I don't pass, then I didn't watch this Tutorial. ~Q ⇒ ~P Either I pass or I didn't watch this tutorial. Q ∨ ~P

[@franciscorodrigues5661]

Vlw

[@maxwellhere8694]

Woah nice shirt

[@jameshurliman8951]

"P implies Q.... because of the implication"

[@EuniceManyetera]

🎉🎉

[@mtaur4113]

If you don't wear flowers in your hair, then you're not going to San Francisco.

[@cayethaniacastillo7248]

this is the weirdest class

[@DrTrefor]

haha ya sometimes:D

[@comedyman4896]

Hahaha, doesn't that seem a little cruel, assuming that someone didn't study hard if they fail? Perhaps they're not lazy but just bad at math.