Discrete Math - 1.6.1 Rules of Inference for Propositional Logic

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: kzread.info/head/PLl-gb0E4MII28GykmtuBXNUNoej-vY5Rz

Пікірлер: 93

  • @TS-wj4im
    @TS-wj4im3 жыл бұрын

    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

    @SawFinMath

    3 жыл бұрын

    Thanks so much!

  • @user-iy4tp2pi6m
    @user-iy4tp2pi6m3 ай бұрын

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

  • @danielm173
    @danielm17311 ай бұрын

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

  • @Articos
    @Articos10 ай бұрын

    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
    @idc206272 жыл бұрын

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

  • @luisrana9801
    @luisrana98012 жыл бұрын

    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
    @JB-tj2ot Жыл бұрын

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

  • @nabeeharehman1140
    @nabeeharehman11402 ай бұрын

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

  • @SMTausif
    @SMTausif Жыл бұрын

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

  • @nicholasdaveta7357
    @nicholasdaveta73578 ай бұрын

    This has been a HUGE help. Thank you!

  • @bogwrangler3424
    @bogwrangler34242 жыл бұрын

    Your cat's meow at 10:47 had my dogs going nuts! haha

  • @SawFinMath

    @SawFinMath

    2 жыл бұрын

    Ha. No cat. That was one of my kids, who was less than 2 years old at the time.

  • @bahar5517
    @bahar55172 жыл бұрын

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

  • @bhaveerathod2373
    @bhaveerathod23737 ай бұрын

    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

    @SawFinMath

    7 ай бұрын

    So happy I could help!

  • @excitedaboutlearning1639
    @excitedaboutlearning16393 жыл бұрын

    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).

  • @Ang-ts6zo
    @Ang-ts6zo2 жыл бұрын

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

  • @SawFinMath

    @SawFinMath

    2 жыл бұрын

    Glad it helped!

  • @weaponkid1121
    @weaponkid11213 жыл бұрын

    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

    @SawFinMath

    3 жыл бұрын

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

  • @hf7822
    @hf782210 ай бұрын

    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

    @Evolution602

    Ай бұрын

    doing the same here now at WGU😂

  • @AjunDev

    @AjunDev

    25 күн бұрын

    @@Evolution602 Same lol

  • @bashalla
    @bashalla3 жыл бұрын

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

  • @ronaldsaunfe7388

    @ronaldsaunfe7388

    3 жыл бұрын

    True

  • @SawFinMath

    @SawFinMath

    3 жыл бұрын

    Thank you!

  • @teemmarley5809
    @teemmarley5809 Жыл бұрын

    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.

  • @mahihoque4598
    @mahihoque45982 жыл бұрын

    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

    @SawFinMath

    2 жыл бұрын

    Happy I could help!

  • @gurjotsinghpandher3908
    @gurjotsinghpandher390819 күн бұрын

    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!

  • @farvamo
    @farvamo3 ай бұрын

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

  • @orgzarsmp4480
    @orgzarsmp4480 Жыл бұрын

    Your video saved my day. Thanks.

  • @asmaarefaatVO
    @asmaarefaatVO2 жыл бұрын

    Brilliant !!!!!!!!

  • @toprakgungor131
    @toprakgungor1316 ай бұрын

    reaaaally good thank you for your efforts and time

  • @soulexesns9522
    @soulexesns952228 күн бұрын

    thank you so much!

  • @bahar5517
    @bahar55172 жыл бұрын

    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 😭❤

  • @rayneng7501
    @rayneng75013 жыл бұрын

    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?

  • @kilrati
    @kilrati Жыл бұрын

    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.

  • @lancepeterclarete6144
    @lancepeterclarete61442 жыл бұрын

    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

  • @bossman4112
    @bossman41123 жыл бұрын

    These are saving me for my midterm thank you

  • @SawFinMath

    @SawFinMath

    3 жыл бұрын

    You are welcome!

  • @ertemeren
    @ertemeren6 ай бұрын

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

  • @Razor20131
    @Razor201312 жыл бұрын

    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

    @SawFinMath

    2 жыл бұрын

    Glad I could help!

  • @tebes9265
    @tebes92652 жыл бұрын

    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?

  • @usmanovais2
    @usmanovais2 Жыл бұрын

    Best teacher to date

  • @maxjohnson8582
    @maxjohnson85829 ай бұрын

    God bless you for actually helping me understand this shit

  • @badass_bloke144
    @badass_bloke1443 жыл бұрын

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

  • @rchimedes
    @rchimedes4 жыл бұрын

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

  • @youssefyoussef3652

    @youssefyoussef3652

    2 жыл бұрын

    hi L

  • @tylerclarke5591
    @tylerclarke55916 ай бұрын

    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?

  • @MegaGamer5454
    @MegaGamer54542 жыл бұрын

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

  • @tojannaiem2671
    @tojannaiem26716 ай бұрын

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

  • @SawFinMath

    @SawFinMath

    6 ай бұрын

    So glad I could help!

  • @akashgola2153
    @akashgola21532 жыл бұрын

    Well explained

  • @Light-ev1dt
    @Light-ev1dtАй бұрын

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

  • @NeelSandellISAWESOME
    @NeelSandellISAWESOME3 жыл бұрын

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

  • @SawFinMath

    @SawFinMath

    3 жыл бұрын

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

  • @mamtasingh8373
    @mamtasingh83734 жыл бұрын

    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.

  • @user-uy3hd2mv9t
    @user-uy3hd2mv9t Жыл бұрын

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

  • @SawFinMath

    @SawFinMath

    Жыл бұрын

    I would just keep a list handy for easy reference

  • @willm3889
    @willm3889 Жыл бұрын

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

  • @teenabu4617
    @teenabu46172 ай бұрын

    Lots of love from India

  • @MikeTheGreatCC12
    @MikeTheGreatCC123 жыл бұрын

    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

    @SawFinMath

    3 жыл бұрын

    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

    @nicklasmunksgaardlarsen2436

    2 жыл бұрын

    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.

  • @titoy3523
    @titoy35232 жыл бұрын

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

  • @waseemqaffaf5715
    @waseemqaffaf5715 Жыл бұрын

    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!!

  • @shayanfreestyle8974
    @shayanfreestyle89742 жыл бұрын

    Queen

  • @SawFinMath

    @SawFinMath

    2 жыл бұрын

    👸

  • @AwaisKhan-lq5gy
    @AwaisKhan-lq5gy2 жыл бұрын

    Much ove.

  • @AwaisKhan-lq5gy

    @AwaisKhan-lq5gy

    2 жыл бұрын

    Love*

  • @davehlave8530
    @davehlave85303 жыл бұрын

    16:35

  • @rutchlyngo1324
    @rutchlyngo13243 жыл бұрын

    🤗🤗💕❤

  • @emerald_eyes
    @emerald_eyes6 ай бұрын

    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

  • @kayd2143
    @kayd21432 жыл бұрын

    7:25 kinda need clarification

  • @SawFinMath

    @SawFinMath

    2 жыл бұрын

    Not sure what you mean.

  • @muhammadahmed2280
    @muhammadahmed22802 жыл бұрын

    Are u fab davis

  • @Death_Metal_Head
    @Death_Metal_Head3 ай бұрын

    I think I'm too stupid to understand this.

  • @burh8651

    @burh8651

    2 ай бұрын

    ong bro, we're cooked

  • @kennyma8526
    @kennyma85262 жыл бұрын

    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

    @SawFinMath

    2 жыл бұрын

    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

    @kennyma8526

    2 жыл бұрын

    @@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

    @kennyma8526

    2 жыл бұрын

    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
    @Ugaritic2 жыл бұрын

    Who came here few days before algebra exam 😭

  • @ronjordan2831
    @ronjordan2831Ай бұрын

    Too many ads

  • @yasminebenyoussef5822
    @yasminebenyoussef5822 Жыл бұрын

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

  • @fullfungo4476

    @fullfungo4476

    Жыл бұрын

    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.

  • @rayyanmahtab513
    @rayyanmahtab513 Жыл бұрын

    This doesn’t make any sense

  • @RenaudAlly
    @RenaudAlly10 ай бұрын

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

  • @tojannaiem2671
    @tojannaiem26716 ай бұрын

    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

    @SawFinMath

    6 ай бұрын

    Glad to hear that