RULES of INFERENCE - DISCRETE MATHEMATICS

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We talk about rules of inference and what makes a valid argument. We discuss modus ponens, modus tollens, hypothetical syllogism, disjunctive syllogism, addition, simplification, and conjunction.
#DiscreteMath #Mathematics #Logic #RulesOfInference
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Hello, welcome to TheTrevTutor. I'm here to help you learn your college courses in an easy, efficient manner. If you like what you see, feel free to subscribe and follow me for updates. If you have any questions, leave them below. I try to answer as many questions as possible. If something isn't quite clear or needs more explanation, I can easily make additional videos to satisfy your need for knowledge and understanding.

[@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!

[@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

[@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

[@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

[@ravisharma1499]

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

[@kirtan2307]

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

[@MsCornyDogs]

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

[@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

[@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

[@mjjeon2292]

I wish I can SMASH that like button irl :)

[@karthikanair644]

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

[@مانجاه]

I second this

[@mohammedsabir5052]

I third this

[@avneetsingh8076]

🤭🤭

[@holly6190]

I fourth this

[@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.

[@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.

[@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 ?

[@alfredpine430]

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

[@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.

[@rossocorsa6577]

5:08 Happy face amazon LOL

[@shivangthakur6046]

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

[@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.

[@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

[@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

[@marckhycs319]

Reviewing for the test later. Last minute!

[@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

[@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

[@ronnaldoobuuundoccc9622]

My mind is extremely confused 🥲

[@RogueViking19]

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

[@Queporquecomo]

I really understood it til I didn’t 🥲

[@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 .

[@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.😂

[@simonegreenidge2702]

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

[@macarenasantillan1404]

Your voice sounds like Jim Halpert from The office

[@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

[@djtygre]

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

[@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

[@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.

[@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.

[@masonspruce1447]

i don’t understand logic when it comes to proofs. i suck at logical equivalences and rules of inference proofs. I NEED ADVICE!!!!!!

[@varionmori709]

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

[@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.

[@arefrufillalshanty4284]

please.. I need help with 1. p∧q→¬r 2. p∨¬q 3. ¬q→p ∴¬r How can we start to solve it?

[@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.

[@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.

[@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.

[@lea-anon]

"if you're taking a psychology course" bro I'm a CS major T-T

[@andremwaura1684]

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

[@indahprimad]

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

[@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.

[@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

[@RAHULTMNT100]

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

[@antwonwalls8611]

Simplification: Why didn't you also include the F?

[@enes5345]

Thanks, where can i find a video about imply introduction

[@cryokal]

YOU are an absolute friccing legend, thanks for this

[@ziadzyad8558]

brother please i have an exam tomorow i will send you the exam and you send me the answers and after i get all point i send you 50 euro

[@rodmaradrianbaingan2448]

[ (pvq)^q›~p] is this disjunctive syllogism?

[@AshleyCifra]

hi can someone explain how did the addition part happen in the last example :

[@randomlee7126]

"cause weRE NOT PHIlosophErs"

[@4203-w9j]

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

[@Dubov1933]

god i can't wait to be done with this class, will never use this.

[@saadatkamaei8829]

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

[@mohamednaeem9111]

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

[@danieldey]

Very helpful, thank you so much.

[@Stalinshounds]

4:20 it's the barber from Courage the Cowardly Dog

[@sahlebrahim121]

i didnt understand 8th step in second example, can anyone please explain??

[@TekTechET]

Thank you for making this video

[@dariusgiannoli8751]

DO you have a video for inference rules for quantifiers ?

[@lasagna-dd]

only the first 4 are the most important as what our instructor said

[@mosaicbrokenhearts2886]

In what year do y'all study this? Me in 2nd year cse

[@addy405]

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

[@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

[@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

[@xgllions2217]

Wish me luck guys on exam tomorrow 😅

[@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.

[@samanthamelton4997]

Some segments in the video are stamped not adjacent to each other

[@Winner221000]

Just curious - I am teaching a homeschool class and they are 8th graders. We are do intermediate logic now and they are not grasping it well. How young is too young to be working with this stuff?

[@Trevtutor]

I don't know if there's an age that I'd recommend. I think it's more about mathematical maturity and experience. Rules of inference might need a lot of real life examples to be understood well, and it also might not be a bad idea to introduce logic puzzles first and then move onto actual mathematical logic.

[@aileenfowler3967]

I just found your channel.

[@subhashinibapatla4405]

Thank you very much. It help us very much

[@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

[@addy405]

Modus Panda these concepts are not easy to lean xd

[@calmfulspider]

step 1: Watches this video to try and understand problem teacher gave step 2: video has same exact problem in it Step 3: ??? Step 4: profit

[@II_xD_II]

solution: make notes to refer during practice time believe me it works

[@nathanmulopo7490]

YOU ARE A FUCKING LIFE SAVER!!!

[@NexGenSlayer]

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

[@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 ♥

[@40BallMilly]

I have no clue what's going on lmaooooooooohelpmeooooooo

[@shreyabhattacharya2644]

Thanks for making it so easy to understand!

[@jackbond2138]

towards the end of the last problem couldn't you use MTT again? like not R implies not S, S, therefore R??

[@bryanyadao2977]

Thank you, God bless. 😊

[@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?)

[@wesalmaswadeh9488]

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

[@vsneelesh3692]

sir can you make videos for rule cp

[@yewyewxd]

does anyone learn this in high school ?

[@hazellorrainedaul5534]

so how about this problem? (p->q)^(pv~r)^(~r->s)^~s->q?

[@reniersteytler1859]

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

[@godofkings4366]

thank you very much. got it

[@musamohannad1598]

Who's here for cpsc 121

[@c-erastustoe212]

simply amazing! Thank you!

[@juliuslinus]

If you're reading this. I know your struggle 😭 we're all gonna pass bro

[@Concon-bu4bp]

Dope video. subbed and liked.

[@shayorshayorshayor]

This guy made all this up.

[@noobsplaysensei3324]

Hope this helps me in my exam too

[@dolokmalau7689]

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