Discrete Math - 1.6.1 Rules of Inference for Propositional Logic

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Building a valid argument using rules of inference for propositions.
Video Chapters:
Introduction 0:00
A Valid Argument 0:07
Modus Ponens and Modus Tollens 3:08
Hypothetical Syllogism and Disjunctive Syllogism 6:01
Addition and Simplification 7:56
Conjunction and Resolution 9:39
Build a Valid Argument Using Premise 12:10
Practice with Me (Assign Propositions) 16:40
Practice with Me (Challenging) 21:45
Up Next 28:19
Textbook: Rosen, Discrete Mathematics and Its Applications, 7e
Playlist: • Discrete Math I (Entir...

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24 июл 2024

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Комментарии : 95

@TS-wj4im 3 года назад

Taking this class online without a professor to explain things has been other than enjoyable. Your videos are making Discrete Math become one of my favorite subjects that I have studied thus far in my Degree. THANK YOU!!

@SawFinMath 3 года назад

Thanks so much!

@danielm173 Год назад

My only regret is not having come across your videos before. May Jesus bless you abundantly.

@doomcake2020 20 дней назад

The challenging example was exactly what I was looking for in order to understand more complicated arguments. Thank you so much, these are fun!

@user-iy4tp2pi6m 5 месяцев назад

You are a life saver and a diamond amongst the rest of most college professors! Thank you.

@Articos Год назад

I know these videos are 3 years old, but as a Brazilian Student that also goes to Discrete Math Class, this is helping me a lot. Thank you Kimberly for helping people all over the world. You are amazing!

@idc20627 2 года назад

HOLY MOLY I JUST STUMBLED UPON AN AMAZING GEM OF A CHANNEL. THANK YOU!

@luisrana9801 2 года назад

Thank you for this! I'm studying in a good university but my teacher here is really bad. You helped me skip a 2-hour lecture and squeezed it on just a few minutes. Thank you!

@JB-tj2ot Год назад

I started enjoying discrete because of you!! thank you so much

@nabeeharehman1140 5 месяцев назад

I was absolutely lost with DM. This is a godsend. Thankyou for this amazing lecture!

@bhaveerathod2373 10 месяцев назад

Omggg I cannot even put into words how much you have helped me!!!! I was so confused about this but I tried the challenging final problem in the video by myself and GOT IT EXACTLY AND I WAS NOT EXPECTING THAT BECAUSE I KNEW NOTHING ABOUT ANYTHING before watching this video! All thanks to you!

@SawFinMath 10 месяцев назад

So happy I could help!

@weaponkid1121 3 года назад

Thanks for making these videos. I go to UNO and these videos are a lot easier to understand than reading the textbook or even my own professor's videos

@SawFinMath 3 года назад

I got my graduate degree from UNO! I had some great professors and a not-so-great one. Glad I could help!

@hf7822 Год назад

These videos follow along with the modules of DM1 in WGU, and you are helping a ton. As the top comment stated, a class that has brought many worries has been turned to such a fun class for me.

@Evolution602 3 месяца назад

doing the same here now at WGU😂

@AjunDev 3 месяца назад

@@Evolution602 Same lol

@Ang-ts6zo 2 года назад

this is insanely helpful, i cant express this enough. thank you sincerely for helping me pass my class

@SawFinMath 2 года назад

Glad it helped!

@nicholasdaveta7357 11 месяцев назад

This has been a HUGE help. Thank you!

@excitedaboutlearning1639 3 года назад

Thank you, Kimberly, for your videos. I finally understood deductive thinking (going from universal to particular: particular being necessarily true when the said particular belongs to the group of the universal), premise, logical symbols etc. thanks to your videos. I also read an article on inductive and deductive thinking on Wikipedia, and inductive thinking clicked as well. The definition on Wikipedia was horrible, but I got that inductive thinking is the opposite of deductive thinking i.e. Going from the particular instance(s) to universal. I also understood that inductive conclusions can never be true but their likelihood of being true can be increased. However even a single instance to the contrary of the conclusion leads to a revision of the conclusion (ideally).

@bahar5517 2 года назад

OMG THANK YOU SO MUCH I REALLY COULDNT UNDERSTAND HOW WE DOING THESE THINGS AND YOU HELPED A LOT THANK YOU

@SMTausif Год назад

thousand times better than my Russian professor. why we dont get professors like you. we could save our time so easily thankyou.

@bashalla 3 года назад

Thank you so much for your great explanations. DM really starts making fun. I wish all my professors could explain Math that way !

@ronaldsaunfe7388 3 года назад

True

@SawFinMath 3 года назад

Thank you!

@debanjanghosal618 Месяц назад

Thanks for the incredible tutorial.

@farvamo 5 месяцев назад

wow, this video really helped explain things much easier, thank you.

@gurjotsinghpandher3908 3 месяца назад

You are so great, I hope I had you as a professor. And just a suggestion in the practice from 16:41 to 21:41, we could have also used hypothetical syllogism to prove the conclusion:) Thanks!

@mahihoque4598 2 года назад

Just want to thank you as a student from bangladesh and being from a middle-class family I can't any tution in these courses the meme's are true youtube does help more than the university in cse thank you

@SawFinMath 2 года назад

Happy I could help!

@toprakgungor131 9 месяцев назад

reaaaally good thank you for your efforts and time

@bahar5517 2 года назад

THANK YOU SO MUCH AGAIN I COULDNT DO IT AND I FOUND IT FEW HOURS AGO BEFORE EXAM AND I DID IT IN EXAM THANK YOU SO SO MUCH 😭❤

@Razor20131 2 года назад

I am a Computer Systems Major - Upper Senior at City Tech. This slides are helping me in advance. Class is online - Spring 2022 but will be on campus once a month. I hope to get an A in MAT 2440. I will also take MAT 2540 in Fall 2020. Thank you very much for posting these videos.

@SawFinMath 2 года назад

Glad I could help!

@orgzarsmp4480 2 года назад

Your video saved my day. Thanks.

@tojannaiem2671 9 месяцев назад

شكراً لالك جداً دورت كثير شرح للدرس هاد بالعربي وبالانجليزي وما فهمته ، بس لما تابعت شرحك الحمدلله المعلومة وصلت وحاسة بالسعادة ..ربنا يسعدك 🙏❤❤❤❤

@SawFinMath 9 месяцев назад

So glad I could help!

@bossman4112 3 года назад

These are saving me for my midterm thank you

@SawFinMath 3 года назад

You are welcome!

@teemmarley5809 2 года назад

Resolution: Just remember p->q has same truth table with ~p or q so, if ~p or r is same as p->r. Therefore we can replace p with r in p or q, which is same as r or q.

@rayneng7501 3 года назад

I would like to ask on your last example, isn't the disjunctive syllabus r v s and not s suppose to give s instead or r?

@ertemeren 9 месяцев назад

It would be nice if there were more middle level sample questions about Rules of Inference.

@soulexesns9522 3 месяца назад

thank you so much!

@badass_bloke144 3 года назад

Why is it modus ponens in the 3rd step of the last example?

@usmanovais2 Год назад

Best teacher to date

@MegaGamer5454 2 года назад

@15:38, how does she use simplification for the second one?

@lancepeterclarete6144 2 года назад

What do you do if you have 4 variables? How can I identify the type of Inferences if there are 4 letters ex; Q,p,r ,s

@tebes9265 3 года назад

Just to make sure I got this right: An argument is the CLAIM that (p1 and p2 and ... pN) imply q. A VALID argument is an argument for that this claim holds. Is that correct?

@maxjohnson8582 Год назад

God bless you for actually helping me understand this shit

@Light-ev1dt 3 месяца назад

Trying to self study here. Just curious, if I have p -> q and not p. Then is the result inconclusive?

@rchimedes 4 года назад

At 15:56, is it ok if I did Modus Ponens first and then simplification to reach the same conclusion?

@youssefyoussef3652 2 года назад

hi L

@tylerclarke5591 9 месяцев назад

for the second example, can we use hypothetical syllogism? p-> not q, -q implies not r, therefore p implies r, then using modus ponens since p is true so is r?

@asmaarefaatVO 2 года назад

Brilliant !!!!!!!!

@kilrati Год назад

Hi Kimberly, I'm a bit confused about the topic of this video intersects with section 1.3.3 (Constructing New Logical Equivalences) . Wasn't that constructing proofs as well? thanks for all the great videos.

@tonynguyen4603 Месяц назад

This is late but for any newcomers 1.3.3 dealt with making two propositions equal, while this video deals with proving that a proposition is true (a tautology)

@NeelSandellISAWESOME 3 года назад

I was confused about your last example. Why does leaving r at the end imply that p->r

@SawFinMath 3 года назад

The first step was q. Using the steps we arrive at r. So q implies r.

@akashgola2153 2 года назад

Well explained

@willm3889 Год назад

If you don't have "q" as a premise. How would you solve this?

@teenabu4617 5 месяцев назад

Lots of love from India

@titoy3523 2 года назад

Good day maam Kimberly! regarding in disjunctive Syllogism, is (( p v q ) ^ ~ p) --> q = ((p v q) ^ ~q) --> p?

@user-uy3hd2mv9t Год назад

Thank you!!! i have a small question, do we have to memorize all of the rules?

@SawFinMath Год назад

I would just keep a list handy for easy reference

@MikeTheGreatCC12 3 года назад

Can someone explain how to get the 3rd step which takes place around 15:10? Why can't you just write q instead of p implies q?

@SawFinMath 3 года назад

You have to have a reason for every step. I can't just say "q" without a logical equivalence. So I have to state the rules I am using. In this case, that is simplification and modus ponens.

@nicklasmunksgaardlarsen2436 3 года назад

I think the video unfortunately is slightly open for misinterpretation in this exact segment unless you observe quite carefully. It also took me a while to understand what was being done. So the rule of simplification that is used was explained in general by p and q as variable names, which unfortunately also were the specific variable names of the logical statement we investigated. So lets instead explain the simplification rule by using myVar1 and myVar2: From the knowledge that myVar1 AND myVar2 is true, we can infer that myVar1 is true (and equivalently that myVar2 is true). Now to take this general simplification rule and apply it to the example, we would recognize myVar1 as p, and myVar2 as "If p then q". Now it must be since that the premise states that p AND (if p then q) is true, it also follows that both p is true, and (if p then q) is true.

@mamtasingh8373 4 года назад

Help professor, I am precisely asking what does the definition of even numbers refers to.Or for simply,the definitions of chairs,tables,spoons etc refers to a class satisfying the stated property or these terms symbolise any object satisfying stated property.

@teole4706 2 месяца назад

I wanna ask a dumb question. Does (q v p) ^ ( h v k) -> q v p true?

@waseemqaffaf5715 Год назад

For the disjunction rule, you took the r. But, according to the formula, u should take the s to be true!? (p or q) and not q then q you did (p or q) and not q then p. Are they interchangeable ?? Kinda confused rn!!

@davehlave8530 3 года назад

16:35

@shayanfreestyle8974 2 года назад

Queen

@SawFinMath 2 года назад

👸

@AwaisKhan-lq5gy 2 года назад

Much ove.

@AwaisKhan-lq5gy 2 года назад

Love*

@Death_Metal_Head 6 месяцев назад

I think I'm too stupid to understand this.

@burh8651 5 месяцев назад

ong bro, we're cooked

@kayd2143 2 года назад

7:25 kinda need clarification

@SawFinMath 2 года назад

Not sure what you mean.

@emerald_eyes 9 месяцев назад

21:52 Can we just say: 1. u→p q→(u∧t) ∴ q→(p∧t) 2. ¬s (p∧t)→(r∨s) ∴ (p∧t)→r 3. q→(p∧t) (p∧t)→r ∴ q→r

@rutchlyngo1324 3 года назад

🤗🤗💕❤

@muhammadahmed2280 2 года назад

Are u fab davis

@kennyma8526 2 года назад

I find that this course video is different and in a different order then my book is. Which mean's if I want to use this to learn I need to finish all 80 videos in 1 to 2 weeks lol cry

@SawFinMath 2 года назад

Or....compare your topic list to the topic list in the book I used. Then watch the videos in the order of your text

@kennyma8526 2 года назад

@@SawFinMath Thank You for answering my response. I am just saying but 1.6.1 to 1.8.2 is hard to follow. I am currently on 2.1.1

@kennyma8526 2 года назад

The college that I am taking is the class "Discreet Math" is know as "Discreet Structures" part of the Computer Science path and the class is called CSC 7 at Riverside City College. They use the discrete mathematics and its applications by susanna 4th.

@Ugaritic 2 года назад

Who came here few days before algebra exam 😭

@yasminebenyoussef5822 Год назад

hello can anyone help me with this one? Premises: (¬p → ¬q),(r → p),(¬r → q) conclusion p

@fullfungo Год назад

Sure, by contraposition law, from (¬p → ¬q) we derive (q → p). Now from (¬r → q) and (q → p) we derive that (¬r → p) by hypothetical syllogism. Now we know that (r → p) and (¬r → p). The last step is the disjunction elimination rule: all we need to invoke is the law of excluded middle (r ∨ ¬r), so (p) follows.

@ronjordan2831 4 месяца назад

Too many ads

@rayyanmahtab513 Год назад

This doesn’t make any sense

@RenaudAlly Год назад

Remembering the names for those operations will definitely kill me. Hypothetical syllogwhatnow? Amazing videos nonetheless of course!

@tojannaiem2671 9 месяцев назад

Thank u for these good lesson I have search abt this subject in Arabic but didn't understand it , but when i see your video i got it ! thank u very much 🤍🤍🤍🤍🤍🤍🤍🤍🙏🙏🙏🙏

@SawFinMath 9 месяцев назад

Glad to hear that