3 Ways to Show a Logical Equivalence | Ex: DeMorgan's Laws

DeMorgan's Laws are two important logical equivalences. In introducing these laws, I talk about three different ways by which you can demonstrate a logical equivalences: There are truth tables, citing known laws, and testing for reasonableness.
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Пікірлер: 76

  • @goransomic3259
    @goransomic32595 жыл бұрын

    dude im paying $3,400 at DePaul Univ. for a discrete math class where the prof. cant explain s***. This has shed more light on the matter than 3 full 3hr courses under her. Thank you!

  • @goransomic3259

    @goransomic3259

    5 жыл бұрын

    Trefor, the first step in th example where you simplify the LHS by DeMorgans law,..are you just distributing the not to the inside of the parentheses and flipping the symbol? i thought since the two ways of morgans law are if not p or q == not p and not q or the second if not p and q == not p or not q,.. since the LHS doesnt really fit in either example,..how is it that we can apply morgans law to the LHS?

  • @mk_4567

    @mk_4567

    3 жыл бұрын

    @@goransomic3259 we consider p and not as the two statements and then apply them to the first theorem

  • @aakashdharmakari2591

    @aakashdharmakari2591

    2 жыл бұрын

    That money is for the degree and not for the teaching services.

  • @AIAnimatedCreations950

    @AIAnimatedCreations950

    2 жыл бұрын

    You are legend 😂🤣🤣

  • @codecleric4972
    @codecleric49722 жыл бұрын

    I'm watching this series to compliment my self-study path of coding/computer science. All of them so far have been great, but I feel like this is where you're really getting into the good stuff. Applying those rules is definitely a cool concept

  • @wintutorials2282

    @wintutorials2282

    8 ай бұрын

    I can give you some recources if you want, im in my first year now

  • @karismaliddell4694
    @karismaliddell46943 жыл бұрын

    Thank you. I'm paying 6,000 at ASU for this class, and these videos are the only way I'm actually going to learn the content.

  • @Brain_With_Limbs

    @Brain_With_Limbs

    3 жыл бұрын

    I'm at UMASS, and having a hard time also with discrete math.

  • @Geb__

    @Geb__

    3 жыл бұрын

    Me too lmao

  • @podi_ta7978

    @podi_ta7978

    3 жыл бұрын

    University is a scam

  • @theyasminroyal

    @theyasminroyal

    3 жыл бұрын

    I go to ASU too lol and same

  • @Aurora-bv1ys

    @Aurora-bv1ys

    6 ай бұрын

    Universities are nothing but a glorified scam

  • @Scuba_Rocky
    @Scuba_Rocky9 ай бұрын

    I agree with a lot of students. I’m taking an online class and the professor too has not done anything and the videos in the modules are boring and don’t explain in details the way you do. You help us build a foundation from the very basics to better understand at a higher level and that’s what being a professor is all about. Thank you so much for helping not only explain but making it fun and engaging enough to WANT to learn and keep watching your videos. Bravo, I wish you were my professor!

  • @derwentsmith499
    @derwentsmith4993 жыл бұрын

    I have to give you a big thanks, my university lecturer struggles to explain equivalences, and watching 3 videos of yours has literally explained everything thanks Dr. Bazett

  • @SEALteam6Operator
    @SEALteam6Operator3 жыл бұрын

    Dr. Bazett, you literally explained this within 1 minute and 30 seconds. That is amazing.

  • @Benedict_Miriti
    @Benedict_Miriti3 жыл бұрын

    This channel is of great help . My lecturers love to complicated simple stuff and make them seem difficult to understand which sucks! Great video Trefor

  • @DrTrefor

    @DrTrefor

    3 жыл бұрын

    So glad it is helping!

  • @osamana7163
    @osamana71633 жыл бұрын

    in 10 mins i understood what my dr. explained in 4 lectures 1 hour each the past 2 weeks

  • @Natluxurious
    @Natluxurious11 ай бұрын

    This video series might be the way I am going to be passing my discrete structures class. Thank you so muchh for this!!!!!

  • @djoleluk
    @djoleluk2 жыл бұрын

    Fantastic explanation with a real-life example, well-done sir. Subbed.

  • @VecrozaDenziba
    @VecrozaDenziba3 жыл бұрын

    Thank you very much, it really help my study. I spent a lot of money for college and yet, i'm prefer this lecture than my professor.

  • @noahrubin375
    @noahrubin3753 жыл бұрын

    You and TheTrevTutor might just be the best thing that ever happened to yt.

  • @MoDiscovery
    @MoDiscovery Жыл бұрын

    This makes way more sense now, thank you for this guide.

  • @august5520
    @august55205 жыл бұрын

    Thank you for the videos they are super helpful

  • @Wildwildmint
    @Wildwildmint8 ай бұрын

    Clear, concise, and simple.

  • @nedas9187
    @nedas9187 Жыл бұрын

    You have an extra bracket in line 3. Great video.

  • @sanamir9886
    @sanamir98863 жыл бұрын

    Thanks a lot for this video. It was very helpful

  • @george4746
    @george47464 жыл бұрын

    Finally, your words are making sense.

  • @aysuergin5848
    @aysuergin58483 жыл бұрын

    THANK YOU FOR SAVING MY LIFE

  • @zaylo9273
    @zaylo92734 жыл бұрын

    how about those with 3 propositional variables? What do we give the third variable? 1100 in truth table?

  • @Moe.firouzabadi
    @Moe.firouzabadi4 жыл бұрын

    Express the biconditional statement p ↔q in a logically equivalent statement form containing only negations (~) and inclusive disjunctions (∨).

  • @George_Kush
    @George_Kush2 жыл бұрын

    Your video quality is great, very well explained, thank you

  • @DrTrefor

    @DrTrefor

    2 жыл бұрын

    Glad it was helpful!

  • @deerealist1
    @deerealist12 жыл бұрын

    My professor did not even take the time to explain this nor break it down as you have. You would think if everyone in the class is missing on the same questions they would realize that they aren't explaining the content correctly. This is appreciated more than you understand. These professors are not explaining it like at all

  • @DrTrefor

    @DrTrefor

    2 жыл бұрын

    That sucks!

  • @wrsflash
    @wrsflash4 жыл бұрын

    awesome , thanks

  • @WebWizGeorgia
    @WebWizGeorgia5 ай бұрын

    good man, I started with different youtube course, next I move to book and I found that youtube course was after that book. your course is different because you are trying to simplifay things and explain it your way which is always better.

  • @Peter-bg1ku
    @Peter-bg1ku4 жыл бұрын

    The only way for me to understand this was using sets...using union as OR and intersection as AND

  • @lahcenechel1855
    @lahcenechel18554 жыл бұрын

    i didnt get the point why the or flip to the and on the minute 4:12 thank you for the help a lot i have an exam coming up

  • @kageemo
    @kageemo3 жыл бұрын

    is there any place whr i can practice this

  • @nInOwarrior0312
    @nInOwarrior03122 жыл бұрын

    Okay, I can just about understand this, thanks

  • @ichmood12
    @ichmood122 жыл бұрын

    thank you

  • @kingkamvoty
    @kingkamvoty3 жыл бұрын

    Can you help me with a problem? I’m a 16 year old dual enrollment student and I’m having trouble.

  • @dagim6625
    @dagim66252 жыл бұрын

    thanks trefor

  • @aziz1558
    @aziz15583 жыл бұрын

    I have a question, if you may. In 4:08 you applied DM law on a statement which contained a double negative. But doesn't DM's law apply to statements which assert, for example, "I am not P nor Q"? i.e. not both? And the statement you applied DM law stated something like: "I am not P, or I am Q" i.e. I am one but not the other. Since a double negative statement is equivalent to a statement that is not negated, how could DM law apply to a disjunction/conjunction with one negated sentence and a non-negated sentence? I am sorry if the question is not clear enough.

  • @manarsalem1685

    @manarsalem1685

    4 ай бұрын

    That's why when he applied DM law he didn't say (not p And not q) but he rather said (not p and not *not* q). I think if you think about it like this, it would click: let ~ q = g and rewrite the question as ~(q ∨ g) then apply DML to get ~q ∨ ~g Now replace g for its original value ~p ∨ ~(g) = ~p ∧ ~ (~ q) that's why he wrote not *not* q. In English imagine it like this: p = Tom is a crocodile q = Tom is not a fish ~ q = Tom is a fish so ~(p ∨ ~ q) translates to ~(Tom is a crocodile or a fish) = Tom is neither a crocodile nor a fish and ~p ∧ ~ (~ q) translates to Tom isn't a crocodile and isn't a fish. or In English imagine it like this: p = Tom is a crocodile q = Tom is a fish ~ q = Tom is not a fish so ~(p ∨ ~ q) translates to ~(Tom is a crocodile or He is not a fish) = Tom is either a fish or not a crocodile and ~p ∧ ~ (~ q) translates to Tom isn't a crocodile and He is a fish = He is a fish okay tbh my reasoning falls apart here and I think that's what you were asking in your question :)

  • @cherulast7998
    @cherulast79984 жыл бұрын

    Men i joined late but its amazing vedio teachers are killing us in school

  • @delealli9965
    @delealli99652 жыл бұрын

    Dude. Thank you.

  • @DrTrefor

    @DrTrefor

    2 жыл бұрын

    You are most welcome!!

  • @StaticBlaster
    @StaticBlaster11 ай бұрын

    Even in English, it makes sense. For example: It's neither P or Q is the same as saying it's not P and it's not Q.

  • @zabanajd6150
    @zabanajd61505 жыл бұрын

    thanks yous

  • @aubreydebruyn84
    @aubreydebruyn8411 ай бұрын

    The analogy made it it click. Where possible please include the real world applications of the topic.

  • @gaiseric9518
    @gaiseric95182 жыл бұрын

    Would ~p∧p just cross itself out?

  • @continnum_radhe-radhe
    @continnum_radhe-radhe Жыл бұрын

    🔥🔥🔥

  • @krispb-2.13.23
    @krispb-2.13.233 жыл бұрын

    The color coding helps.

  • @mohammadyahya78
    @mohammadyahya782 жыл бұрын

    Thank you. When you are given : 10. Which of the following set of expressions is not equivalent to each other? a) 𝑝 and (𝑝 ∧ 𝑞) ∨ (𝑝 ∧ ¬𝑞) b) 𝑝 → (𝑞 → 𝑟) and (𝑝 ∧ 𝑞) → 𝑟 c) (𝑝 → 𝑞) → 𝑟 and (𝑝 ∧ 𝑞) → 𝑟 d) All of the above are correct How you would solve the above in less than ONE MINUTE please? Using truth table will take a lot time, so I don't think it's recommended here.

  • @fredboytv1257
    @fredboytv12573 жыл бұрын

    need help plss.. Note : * Determine whether each pair of statements is logically equivalent* 1. ~(~p --- q) and p --- ~q note --- is Implies 2. ~(p or q ) and ( ~p) V ( ~q) 🙏🙏🙏🙏🙏 thanks.

  • @katedvaliant4116

    @katedvaliant4116

    3 жыл бұрын

    Hi. I don't know if it was too late but the two statements are not logically equivalent. I used truth tables to determine it. P. s. I am also a student so correct me if I'm wrong

  • @akoymensahero5111
    @akoymensahero51112 жыл бұрын

    Dr. Terfor good day! I just want to ask a question about this topic. I probably need your help. It can be verified that if p and q are statement then A. (Left side) ~ (p^q) = ~pv~q (right side) B. (Left side) ~(pvq) = ~p^~q (right side) Use this equivalence to rewrite the statement. YOU ARE NOT SINGLE AND NOT THE HEAD OF A HOUSEHOLD. So Dr. Terfor what could be the answer of this situation , I want your help. It could be? A1. (Left side) You are single and the head of a household. A1.(Right side) You are single or the head of a household. B1. (Right side) You are single or the head of a household. B2. (Left side) You are single and the head of a household. Am I right Sir? I hope for your response. Thank you so much in advance!

  • @mzhdataha4921
    @mzhdataha49212 жыл бұрын

    👏

  • @flame2179
    @flame21792 ай бұрын

    Bro if you became a lecturer your class would always have top grades

  • @guyincognito7211
    @guyincognito7211 Жыл бұрын

    It is all the sort of thing that I learned at my grandmother's knee

  • @TromCrabst
    @TromCrabst2 ай бұрын

    Wait, "~" is spelled "knot"? I assumed it was just "not" since it kind of means the same thing haha

  • @turupofficial4125
    @turupofficial41253 жыл бұрын

    2021🤠

  • @Benjamin_Bryant
    @Benjamin_Bryant2 жыл бұрын

    Great video mate. Really unfortunate spelling of ur name, u must get Trevor a lot

  • @_baseer_
    @_baseer_3 жыл бұрын

    wow.

  • @salehsssso
    @salehsssso3 жыл бұрын

    أبلع لايك ❤❤

  • @nervcvda6146
    @nervcvda61463 жыл бұрын

    I am unable yo.join Chanel Help me

  • @DrTrefor

    @DrTrefor

    3 жыл бұрын

    Hmmm weird. There is a button called "Join" beneath each video, what happens when you go through that?

  • @nervcvda6146

    @nervcvda6146

    3 жыл бұрын

    @@DrTrefor i got it what was happening

  • @nervcvda6146

    @nervcvda6146

    3 жыл бұрын

    @@DrTrefor but i have a problem For Payment i don't have theSe Cards For Payment

  • @teachforyou8384
    @teachforyou83844 жыл бұрын

    Nice teacher I'm from india

  • @bennyuchiha8501
    @bennyuchiha85015 ай бұрын

    Just flip it

  • @reginarahamathullah828
    @reginarahamathullah828 Жыл бұрын

    Translate in tamil plz🙏🙏

  • @MineCrafterCity
    @MineCrafterCity10 ай бұрын

    But imagine writing such dumb if statements... I don't see why we would need this at all.