RULES of INFERENCE - DISCRETE MATHEMATICS

[@Trevtutor]

Check out my new course in Propositional Logic: trevtutor.com/p/master-discrete-mathematics-propositional-logic It comes with video lectures, text lectures, practice problems, solutions, and a practice final exam!

[@JoseAlvarez-dl3hm]

Thank you a lot, you saved me. My college professor has a lot of knowledge but he likes to make the logic course overly complicated and abstract, not teaching anything at all. You have saved my course.

[@aileenfowler3967]

Same here, we are the ones to find the solution to the dilemmas.

[@SirCruxr]

0-1000 from the first example to the second example

[@andremwaura1684]

i swear......we need more examples...any suggestion videos?

[@shayorshayorshayor]

​@@andremwaura1684 "discrete math examples" on KZbin

[@MsCornyDogs]

This really solidified things for me. I was confused about this part in class, thank you!

[@RJ-sx6ti]

I hope this video will help me for our exams tomorrow. Wish me luck guys

[@Anuramalok]

I too have exam of logic tomorrow good luck to us

[@amyfong1992]

Jorge Martinez, II I have it this Friday lol

[@going_dark]

tommorow

[@RJ-sx6ti]

@@gpakkol6682it turned out well

[@rolexshadow]

mine begin in 3 weeks from today

[@craiggray7110]

Thank you TrevTutor I believe you really do help a lot of people that previously did not have the opportunity to study further due to financial issues or time constraints etc.

[@tasfiaalam84647]

Hi, I am confused about when we can use addition (as in example 2 for step 8). Why do we introduce addition and when do we use it in general?

[@kaminvdi]

(To my knowledge) Anyone who may need this in the future: Addition can be used to make a statement bigger. I saw a great example where it's explained like: Jackie likes pancakes (Premise). Use addition to say Jackie likes pancakes OR dirt. It doesn't matter that Jackie doesn't like dirt, because the Jackie likes pancakes is true. He is adding NOT L to NOT S so that we can use modus ponens to prove that "R or F". NOT S or NOT L --> R or F (this is from line 6/7) NOT S or NOT L (Got this from adding NOT L to the end of line 4, NOT S. Doesn't matter if NOT L is true or not. It's an or statement) Therefore, R or F must be true. Word example: if Jackie doesnt like candy or doesnt like pears, then she likes apples or chips. Jackie doesnt like candy or doesnt like pears. Therefore, jackie likes apples or chips.

[@ElvisSikapi]

Would it not be "Jackie likes apples AND chips instead of OR? I dont know if I misunderstood. @@kaminvdi

[@catherinesalazar2113]

TrevTutor saving my DM univerisity module 6 years before it started! THANKS SO MUCH ! It makes so much more sense when explained like this ♥

[@Elantry]

This is golden! Thanks for mentioning the NAMES of the methods, my teacher just calls them "figure 1.11 lemma 12" and so on. So confusing.

[@karthikanair644]

You're an amazing teacher! With such a soothing voice :)

[@مانجاه]

I second this

[@mohammedsabir5052]

I third this

[@avneetsingh8076]

🤭🤭

[@holly6190]

I fourth this

[@TheViceDynasty]

I'm gonna need you to make the way you wrote "contrapositive" into a font because it looks so satisfying.

[@addy405]

contraceptive is a better word :P

[@haiderbangash99]

The grate work when you help people forever . The grate work sir done its since 4 year people are still using this video. 🙏🏻😍😇 and have a easy method .

[@ravisharma1499]

"Yeah, it's not always super straightforward " Hey, woah, easy with the big guns.. ouch. Really awesome lecture, tho, thanks man..

[@Idan-tc5rt]

You're a beast. Can you please make a video about turning formulas into DNF or CNF (not necessarily full) without truth tables ?

[@مانجاه]

u found one yet?

[@basam1459]

​@@مانجاه he is properly died by now if u want a website that can turn DNF to CNF or CNF TO DNF. massage me

[@jaividyasagarr7110]

@@basam1459 ya send me the link here

[@alfredpine430]

I LOVE YOU SENSEI 😍😍😍 this is the easiest to understand explanation

[@TheGheezoinky]

Hi, you're an amazing teacher. Without you my discrete structures course would have been a complete nightmare. I have liked, subscribed as well as shared it with my whole Discrete class. :D Keep up the good work, sir. :)

[@Abdelrahman-qm9sp]

انت كنت aast ?

[@mohamednaeem9111]

You are the best tutor I have ever seen, Good Work, Thanks indeed and wish you a happy wonderful life!

[@Th1sUsernameIsNotTaken]

I feel like text books skip the parts that make a lot of rules in math make so much more sense when mentioned by a person. I read all of the rules from mine and was just like "...." This made them make more sense by adding a few words the books left out lol.

[@benthomas6828]

Thank god for KZbin and good people like you. My professor runs through this stuff in about 2 min and then just expects us to know how to do proofs like the last one you did.

[@FM-wp8ut]

You're the best. I almost gave up on this math class. Thanks to you. I am starting to understand the concepts.

[@II_xD_II]

12:15 did you guys saw he wrote simp

[@Jjaro7515]

bruh

[@II_xD_II]

@@Jjaro7515 i was kinda drunk lol not really

[@djtygre]

this video is great, really helped me out. loved the hard example at the end and how simple you make it.

[@miarwh]

I didn't understand step 8 where you used 4 and addition, how did you know that you need an addition and why you chose "not S" with "not L"?

[@Trevtutor]

Because I wanted to use Modus Ponens to get to the consequent and finish the proof. The rules never tell us what to do, but they tell us what we can do. We still have to keep in mind where we're trying to go and what we can do to get there when we do these proofs.

[@johanronkko4494]

Mia Q, if you use the conditional law on step 6 instead of the DeMorgans law, then on step 7 use the DeMorgans and Double Negation, you will get the following result: (S AND L) OR (R AND F). Then you can apply the Disjunctive Syllogysm from step 4 and 7 to get (R AND F). From there you use the Addition Law and get R. This is not the approach TrevTutor used but I thought it might be good to see two examples to grasp the addition.

[@thegamesurfers9130]

Johan Rönkkö *McCarran

[@zethesmade]

you're right johan ronkko (that's not confusing)

[@javaexpertsa8947]

Johan Rönkkö You made some mistakes. :) From (R AND F), you don't get R with the Addition Law, also there was some other mistakes.

[@materialknight]

Here's another, slightly longer, proof of the second example: 1. (ㄱR∨ㄱF)→(S∧L) Premise 2. S → T Premise 3. ㄱT ∴ R Premise & Conclusion 4. ㄱS 2,3 MT 5. S∧L assumption for Indirect Proof (Reductio) 6. S 5 Simplification 7. S∧ㄱS 6, 4 Conjunction 8. ㄱ(S∧L) 5-7 Indirect Proof (Reductio) 9. ㄱ(ㄱR∨ㄱF) 8,1 MT 10. ㄱㄱR∧ㄱㄱF 9 DeM 11. R∧F 10 DN 12. R 11 Simplification

[@nielsnielsen1360]

I know you posted this a while ago but I want to thank you anyhow. This reply helped me check my own work and also gave a really great example of how to post a clear to read proof inside a youtube comment. I wasn't sure how to communicate what i was writing on my notebook when typing things out and this reply really helped clear things up.

[@materialknight]

@@nielsnielsen1360. I'm glad to read that! :D It's really cool when you receive positive feedback on something you didn't even remember you had written xD; also, I get to see my past comments and feel as if they were mine but from someone else.

[@dumbcat720]

can you help me with my assignment

[@indahprimad]

Thank you for your explanation. It is easy to understand.

[@cryokal]

YOU are an absolute friccing legend, thanks for this

[@gwoody20]

Finally, it took four separate explanations for me to figure it out. Thanks!

[@erwinleo7337]

for the last question you can also to this type of process. 1.) 2,3,MTT 2.) 1, result of 1.), MTT. 3.) De Morgans, 4.) Simplification. That's it.

[@marckhycs319]

Reviewing for the test later. Last minute!

[@RogueViking19]

amazingly detailed! cleared all my confusions. Thank you so much!

[@addy405]

Thanks watching this a few times it starts to make more sense :D

[@kirtan2307]

Who are the those guys who didn't understand 2nd example 😕

[@RAHULTMNT100]

thanks. you explained it very well... really gonna help me for tomorrow's test!

[@sosihaile6372]

i used fewer steps in the last exercise: ¬s is true so s ^ L = F which would make ¬R v ¬F also F for premise 1 to be true which means both ¬R and ¬F are False which makes R true. i'm not sure what specific rules would apply for each step though

[@captainfoodman]

For those of u who didn't undertsand line 8, he took line 4 "~s" and applied addition law to that. this will get us (~s or~l). then applying this to line 7 we get line 9.

[@nhelcidjanbalabbo4938]

But why use l instead of any letters

[@HAAH999]

Could you please provide an additional sheet of Q&A for this video. It was very interesting and would love to have some practice with more examples

[@garyhughes1664]

This was a great introduction and I followed it well up until that second example which had me totally flummoxed, though I can see how you got there. Thx for sharing.

[@spacesuitred3839]

(Best of all time )discrete math videos!!! keep going!!!

[@shreyabhattacharya2644]

Thanks for making it so easy to understand!

[@omarmenjivar1563]

I greatly appreciate all the you're doing to help teach those who come asking for help.... but DAM. This is still not enough.

[@andreigeorgescu277]

At 11:30 , can you please explain the addition step? For addition to work, you must have ~S and ~L alone, but only ~S was alone so where did the ~L come from? Thank you.

[@cobravideos4636]

he is referring to step 4 not 7

[@andremwaura1684]

this was really helpful.....but could you make an examples video for these rules of inference?

[@sampah89]

This is the very video if everyone watches and masters the world will be a much better place.

[@subhashinibapatla4405]

Thank you very much. It help us very much

[@danieldey]

Very helpful, thank you so much.

[@anmolbansal5010]

Excellent explanation bro!!! Loved it.

[@yamatanoorochi3149]

what I did was this: Modus Tollens like you started then I took ~S, and used it to show that (S and L) is wrong therefore we have ~(S and L) [(~R or ~F) => (S and L)] and ~(S and L) therefore ~(~R or ~F) therefore R and F therefore F therefore R

[@emerald9054]

Thank you so much for this video and the whole course! My teacher cannot hope to be as good at teaching as you are. Do you think it's possible to do the last problem without the logic laws and only the rules of inference?

[@Trevtutor]

Yes, but we'd need a few more rules to make it work.

[@TheGheezoinky]

TheTrevTutor Just wanted to jump on the thank you bandwagon! Great work man, you have really helped me out in my Discrete Structures course. Thank you so so much :) I hope you're profiting off this service in some way or another if that is your ultimate goal. Anyways, kudos.

[@bryanlowks6117]

awesome introduction to this topic!

[@ravipriya5412]

Tq sir I can understand only rules not problems plz upload more problems....

[@4203-w9j]

broo tysm, i'll def be coming back to this!

[@TH3Willster]

Awesome video man, by chance the examples you went over were in my tutorial today and it all makes sense now

[@reniersteytler1859]

Thanks for much for this. Do you have some material for rules of inference for quantified statements

[@MrCommenter1272]

Shouldn't 8. at 11:34 be Implication Elimination?

[@balramchary5622]

Nice explanation 😊

[@snotface8]

Automatic sub.... Thanks man you really came through clutch with this video.

[@TekTechET]

Thank you for making this video

[@felinomancer]

This is a really great video and I'm glad I watched it; but I feel the premises should be in lower case, since in the last example I thought the F is a premise instead of False.

[@c-erastustoe212]

simply amazing! Thank you!

[@bryanyadao2977]

Thank you, God bless. 😊

[@noobsplaysensei3324]

Hope this helps me in my exam too

[@خالدالابيض-د2ت]

i hope this video will help me for the exam after 2 hours. I am hopeless dude

[@saras2367]

How was your exam? 😣 I can't understand it at all. I'm hopeless, too.

[@MaxibillianBus]

what is life man

[@خالدالابيض-د2ت]

@@saras2367 I dropped the course, hopfully i will take it in another noncorona semester.😂

[@NexGenSlayer]

How do you know that its a tautology though unless it says so or if you use a truth table to prove it...

[@varionmori709]

At 3:00 - "Cause you know.. We're Discrete Math people!.. Not philosophers.." LOL 😂🤣

[@dariusgiannoli8751]

DO you have a video for inference rules for quantifiers ?

[@asimpleton135]

For number 5, could you use MTT on 1 and 4 as well to get R and F?

[@spamkaze]

In the second exercise, I used not(s^l) for step 5, allowing me to reach the conclusion in 8 lines instead of 10. If you already have not(s), then you automatically have not(s^l), yes? Is there a name for that rule, or is it just the definition of and?

[@asap397]

not(s^l) isn’t logically equivalent to not(s) not(s^l) is logically equivalent to not(s) [or] not(l) That’s by DeMorgan’s Laws. That was a good try though definitely insightful

[@gopikagopu1194]

good way of teaching

[@LilMtn0011]

Very nice video with a clear explanation. I'm curious about the app you use for this "whiteboard". Much clearer than what I have.

[@Brian-fe2fb]

I guess it would be easier to understand inference as the process of elimination of possibilities in truth tables. The way I learn inference is by using truth table.

[@danielchangsp]

Nice video, thanks alot

[@davidzima659]

Have a problem with example 2 in step 8. Where are disappeared R^F?. Because additional is when you have one leter P after you get it P or Q.

[@timothyryan8753]

So are we just assuming every proposition is true when doing these proofs? My book didn’t explain this at all, the video wasn’t entirely clear either but did help. My mind is trying to consider every possible value for each prop and it’s pretty overwhelming and not well explained

[@anasnadeem40]

12 hrs to go..... Thanks :')

[@Trevtutor]

Good luck!! You can do it!!!

[@wesalmaswadeh9488]

The last example We can use 1,4,Mtt And that give us ~(~r OR ~f) Did it work? Then use the simplification

[@shivangthakur6046]

"Modus ponens" and "Modus tollens" both sound like spells from Harry Potter!!

[@nikkisu3065]

would it be a valid step to go from ~ (S^L) --> (R^F) to ~S --> (R^F) & ~L --> (R^F) using ^E/Simplification as the justification? Or is that illegal (and if it's illegal, why?)

[@rossocorsa6577]

5:08 Happy face amazon LOL

[@usmanahmed1267]

You are love broo!!! Thanks for that

[@intentionalvideos456]

Take S implies T and ~s then apply modus tolens then ~T is the result, Is this correct ?

[@jacobwharton5048]

no. Modus Tollens is applied when you have propositions in the form: (S->T)^(~T) which implies (~S) (essentially contrapositive reasoning applied to Modus Ponens). With the propositions you have supplied, I am pretty sure that there is no logical inference that can be made.

[@j-dope6536]

9:00 Thank you!

[@Concon-bu4bp]

Dope video. subbed and liked.

[@dolokmalau7689]

Hello, in simplification if the premise are ~p ^ ~q, then what is the answer ? is it ~p ? thank you so much.

[@JuliusMghendiCreations]

that was awesome. points well explained and easily understood. Thanks so much. would you kindly help me proove the first absorption law using truth tables. Thanks in advance

[@godofkings4366]

thank you very much. got it

[@simonegreenidge2702]

Excuse me while I play this over 100 times til I get it

[@Steve168xyz]

u r the best

[@fengbeilingwang677]

In the last example, why isn't R and F considered F using Domination Law? I am confused. Thanks for answering!

[@asap397]

Fengbeiling Wang assuming you mean simplification by “Domination Law,” you could conclude F from R ^ F. But that’s not really useful for our problem here since the problem asks us to conclude with R and not F

[@andrewryabinin7341]

Can we use Simplification Rule in place or we must have a separate premise to use it? For expample: (not R or not F) then (S and L), are we able to convert this to (not R or not F) then S?

[@TheThiaguw]

A premise is needed. When you don't have the premises, you use the simplification because you are treating all the lines of the truth table. When we use rules of inference, we are only interested in one line of the truth table, the line which obey the premises.

[@hieunguyenthang3535]

more meaningful thanmy in - class lecture

[@spacesuitred3839]

in the last example, if we would entail L would we write L as an answer?

[@srinivasraman50]

Thank you so much. Really helpful

[@abhijeetsharma5715]

In the 9th step, you wrote "R AND F...but because of the F, it can't be True...how can we even proceed from there?

[@Trevtutor]

F in this example isn't "contradiction" like it has been before. It's just a statement like A, B, C, etc. Perhaps not the best letter to use in this example.

[@KeiS14]

6 years late and 30 minutes of checking through comments and prior videos later, I have to say, “F wasn’t meant to stand for False” was not the solution I was expecting

[@shanaexcalibur]

My lecturer requires only the use of inferences not the laws of logic is there a way to do the last question using laws of logic?

[@stephenaraka5870]

thanks TheTrevTutor.

[@jerushanmoodley2641]

well done @thetrevtutor

[@enes5345]

Thanks, where can i find a video about imply introduction

[@aion2177]

superb explanation! Thanks :D

[@vatsalgupta6889]

Check it is valid or invalid?? If the two sides of the triangle are equal then opposite angles are not equal .Therefore opposite angles are not equal

[@OmarAbdelhak71]

What is the app you are using