I am a 72 year old retired electronic engineer and software engineer where anything can be built with a tiny set of AND, OR, NOT gates. My old professors chose to teach us electromagnetics instead of discrete mathematics. I now find myself needing to understand discrete mathematics. I'm struggling to connect the dots with my old Boolean Algebra. I know they connect, but I'm not there yet. Looking forward to understanding. Thank you Professor Brehm.

I have never learned discrete math before and is having a difficult time during lectures, thank you so much for this great explanations and detailed notes that gradually help to let all these to make sense! Really appreciate it:)!

@SawFinMath

2 жыл бұрын

Thanks! Glad I could help.

I burnt out halfway through this semester, and this class is the one I’ve gotta study for. Thank you very much.

After thinking about this, it appears that discrete mathematics is exactly the same as my old days designing digital systems. The terminology is a somewhat different. FYI, in electronics we call the XOR logic gate "exclusive" OR. It's satisfying to begin understanding. Thank you Professor Brehm.

I was late from my uni for 6 weeks of lessons because of some enrollment issue, so I decided to learn my courses by myself online and found this channel, you are the best prof! if my courses are in italian then i can't understand them, p -> q if I can't understand them, then my courses are in italian, q -> p (converse, switch order) If my courses aren't in italian then I can understand them, -| p -> -| q (inverse, negate) If I can understand them then my courses aren't in italian, -| q -> -| p (contrapositive, switch order then negate)

@emailemail4801

Жыл бұрын

Hey I'm in your situation now this year how are you doing now

@Aremote

3 ай бұрын

Hey@@emailemail4801 im in your situation this year how are you doing now?

You are so good at explaining! Thank you so much, because i do not have lectures at university, only practice lessons, so you are like my only lector and i am glad i found your videos

That was a delightful exposition to the essential concepts such as contrapositive, converse, and inverse coupled with implication and the biconditional. Thank you.

To say that this is informative would be an understatement!! I am in my fifties learning how to code and this video series shores up a lot of the things that previously baffled me. Thank you and bless you, Professor Brehm!!!

@SawFinMath

Жыл бұрын

Thanks for watching! And best of luck to you in your studies!

Thank you for the videos. I really love the way you simplify the subject.

thank you , the best lectures in discrete mathematics

getting into math and starting with teaching myself discrete math your explanations are great i'm able to listen and understand

what a beautiful NOTE !! ;) the contrapositive is the inverse of the converse.

I learned most of this course by watching your videos and I find them very well organized and you explained things very well. You helped me get 100% for my 2 exams. Thank you so much!

@SawFinMath

Жыл бұрын

That's awesome! Glad I could help!

Great lesson! Learned a lot! 😊

i like the way you explain the lecture its easy thanks so much

Great lesson lovely Prof. B

thank yo so much, you're the best

I'm a bit confused about the professor b example, would it not be if professor b is happy then you completed your homework when you make the original statement into an if then statement. Or would p-->q be the same as q-->p

awsome video, thank you very much

The notes look great. Is there a recommended companion DM textbook? I have found several free open source books.

Thank you for making fantastic exam review content

@SawFinMath

Жыл бұрын

So nice of you

Thanks. The implication is tricky indeed

FYI students: Discrete mathematics represents the underpinnings of software/computer/electrical engineering. If you're going into any of those fields then this is the most important math subject you will ever learn. It literally defines the entire profession.

Professor I believe there is a mistake on the biconditional slide, wouldn't it be "q if and only if p" instead of "p if and only if q" ?

Do we need any prerequisites to comprehend the whole course? I am not a math student. I haven't seen integrals or such. I wonder if I need any further knowledge to comprehend the whole course.

@front331

3 жыл бұрын

At my university, the pre req for Discrete Math is Pre Calculus and Calculus. Which is a bit strange I think because at community college, Discrete Math has a higher value than Calc III. But I think this class is the foundation of whether students want to pursue math or not. And Calc III was surely difficult but was culmination of all the maths learned up to that point. And of course didn't help that it was in 3-D.

@WickedTwitches

3 жыл бұрын

Looking at the content, you are probably fine but it some of it may be difficult. Should you learn calculus to supplement what's in this, yep.

@ashk3734

2 жыл бұрын

@@WickedTwitches don't need calculus

13:23 So by "truth values", we mean "the value of each proposition", regardless of whether the "truth value" is actually "true" (Therefore, "false - false" are the same "truth values"). Did I get that right? Thank you professor B!

@SawFinMath

Жыл бұрын

Yes. We are talking about "truth values" as true and false. Not just true.

@ulysses_grant

Жыл бұрын

@@SawFinMath Great. Thank you professor!

So is the same addressed for implication of P = False and Q = True? I understand that if P = False then Q is always = True. What is the vice versa?

For the practice problem of the statement "Prof.B is happy when you complete your homework.", why would the if/then form not be "If Prof.B is happy then you completed your homework."? I am a little confused why one is correct and the ohter is not

@ThomasEdits

8 ай бұрын

6 months late but commenting in case others are wondering the same Notice how the premise can be rewritten as «when you complete your homework» «prof b is happy» in other words if «completed homework» then «prof b is happy» Basically the homework part is the «action» part and the happy professor part is the «reaction»

What would be inverse of bioconditional?

thanks a lot mam

Can you define , ' p unless q ' , using propositional logic, with an example. I want to analyze the statement _Jack plays golf unless it rains_ . Let p = " Jack plays golf" , q = " it rains" . Then "Jack plays golf unless it rains" = p or q ?

@breadcrumbstories1

Жыл бұрын

Learning as I go, so this is super late (but helpful for me to answer). I'd just rewrite it has If it doesn't rain (p) then jack plays golf (q).

Hi there. So during implications, the last sentence in the green text says "When the hypothesis is false, the conclusion is true.". Now, the hypothesis is p, and the conclusion is q. Which means, "When p is false, q is true.". So wouldn't that make q true in the last row? Or did you mean to write 'implication'? Because then it would mean "When the hypothesis (p) is false, the implication (p -> q) is true." Which would make a lot more sense.

@bisonfacelove

3 ай бұрын

ik you posted this a while ago so you probably already figured this out, but this is actually a super common mistake so i’ll answer regardless. First off, it’s important to note that the truth of a statement like (p->q) has no effect on whether the variables (p and q) are present. In truth tables, the Ps and Qs in each row are set parameters used to evaluate the statement in various conditions; because of this, the variables imply the truth of the statement, but the truth of the statement does Not imply the truth of each variable. Now, as for why F+F equals T, that lies in the decision some random person years and years ago made to emphasize “T until proven F” over “F until proven true.” Theoretically you could have F+F imply F using the latter line of reasoning, but because in truth tables we for simply don’t, the reasoning goes like this: “if a statement is not contradicted, it is not proven false; since the binary of T or F leaves us only one other option, it must be true.” (I don’t like the reasoning T until proven F, but it is just as reasonable as the other when an ultimately inconclusive result needs to be assigned a value within a binary.)

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can anyone tell me why isn't it "False" in the second row of "q implies p"? for example if we say that: if you get 100 in the final then you will get an A+ in the course. here "p"represents: you get 100 in the final "q" represents :you get an A+ so when we say that q>>p while Q is false and P is true if you didn't get an A+ in the course then you get a 100 in the final !!! It doesn't make sense at all !!!!!!!

@naret03

2 жыл бұрын

I don't know much about this subject so take my comment with a grain of salt, but here's how I understand it. I like to think of implications are valid or invalid rather than true or false, so like you said, if I get an A+ in the course then I get a 100 in the final is a valid implication. If I get an A+ in the course then I don't get a 100 in the final, is invalid since an A+ guarantees a 100. If I don't get an A+ in the course then I get a 100 in the final is still a valid implication, maybe I got an A++, or the teacher uses a different system where from A and upwards is equal to 100. And lastly, if I don't get an A++ in the course then I don't get a 100 in the final, is a valid implication, maybe I got a B and a 85 in the final.

@Idontgiveashit189

2 жыл бұрын

If you are talking about the final truth table in the preview: Since q -> p is an implication, it doesn't matter that q is false since it is the premise (the first proposition). If the premise is false and the conclusion (q, the second proposition) is true, the whole implication is by definition also true. I know it doesn't make much sense but as much as I have understood it, it is so.

@justintheballer3733

2 жыл бұрын

I just had the same question! Thanks for commenting on it

Just a quick question, does inconclusive means true?

@SawFinMath

Ай бұрын

Inconclusive means that we cannot draw a conclusion.

Book has the following question. Write the following statement in the form “if p, then q” in English: 'To be a citizen of this country, it is sufficient that you were born in the United States.' The book says that the correct answer is "If you were born in the United States, then you will be a citizen of this country." Shouldn't the correct answer be: "If you are a citizen of this country, then you were born in the United States." Because "p is sufficient for q"

@samuelokon8842

3 жыл бұрын

The book is right. The general form "for p, it is sufficient that q" is the same as " if q then p" which is also the same as " q is sufficient for p"

@donpathirage5804

3 жыл бұрын

@@samuelokon8842 Thank you for the reply. So, you are saying both, "If you were born in the United States, then you will be a citizen of this country" and "If you are a citizen of this country, then you were born in the United States." are correct? Basically, you can switch p and q around the keyword "sufficient".

@samuelokon8842

3 жыл бұрын

@@donpathirage5804 No that's not what am implying. The general idea is that saying "a proposition, p is sufficient for another proposition, q" is equivalent to saying "if p then q". But lets now analyze the problem at hand: "To be a citizen of this country, it is sufficient that you were born in the United States.". This has the same meaning as that "being born in the United States is sufficient for one to be a citizen of the USA" which is equivalent to saying "If one is born in the USA then he or she is a citizen of the USA". Note the above statements is not equivalent to saying "If you are a citizen of this country, then you were born in the United States.". Because one may be born outside the USA but still be a citizen of the USA( This could occur if his parents are citizens of the USA or he is an immigrant that had been awarded citizenship by the USA). So the basic issue here was converting the English sentence into logical grammar. (English has ambiguities that makes it unsuitable for discussing complex mathematics)

@samuelokon8842

3 жыл бұрын

@@donpathirage5804 Sorry if took me so long to reply you.

@thezeneris

2 жыл бұрын

@@donpathirage5804 "To be a citizen of this country, it is sufficient that you were born in the United States" is the same thing as saying "You were born in the United States is sufficient to be a citizen of this country". From this form it should become more clear that "If you were born in the United States, then you will be a citizen of this country".

A question regarding the material beginning at 11:10, if you don't mind: The original implication is said to be "If you complete your homework, Professor B is happy." In the video, the converse is written as "If Professor B is happy, then you completed your homework." Why would the converse not be "If Professor B is happy, then you complete your homework"? Perhaps I am reading too much into it, but the change in verb tenses within the converse, inverse, and contrapositive is throwing me off. Obviously, the video's version makes more sense in plain English, but it appears to me that the actual converse, based upon our propositions p and q, should be the literal "If Professor B is happy, you complete your homework."

@a.human.

2 жыл бұрын

You're right. She mixed up the inverse and contrapositive in this one.

Why don't you add PDFs files for all lessons. That's would be great!

@SawFinMath

4 ай бұрын

I give you access to all of the power points I use. You can certainly create pdfs from those!

@relytheone853

4 ай бұрын

@@SawFinMath Yeah! Nice!

kzread.info/dash/bejne/pHWsusWRj9qblqg.html why isn't the statement when I write it in Implication form, If Prof B. is happy then, you completed your homework then go from there to write it in converse, inverse, and contrapositive?

@crazysox305

2 жыл бұрын

that's what im wondering too. maybe it doesn't matter either way, since the contrapositive and original statement have the same truth value. but i think it might be split up into 1) the triggering event and 2) the outcome of the event. in the first example, raining is the triggering event and not going into town is the outcome. they are assigned p and q accordingly. in the second example, completing the homework is the triggering event and prof b being happy is the outcome. these two things are also assigned q and p accordingly. idk if she does it that way bc it's the only correct way to do it or bc it's her preference.

Hello Professor. I think you made an error at 11:47 , it seems to me you mixed up the inverse and contrapositive in this one. Hope you add a note so students don't misunderstand. Great lecture and amazing series regardless :)

@Clown-su5ym

2 жыл бұрын

um I dont quite understand, could you explain a little bit?

@sirpsychosexy

2 жыл бұрын

No I just double checked it, those are correct.

IFF

miss girl monetized TF out of these videos... so many ads

@SawFinMath

7 ай бұрын

‘Miss girl’ doesn’t feel bad about that since all of the money goes to her children’s’ college fund

Discrete Maths More Like Easy maths

So many ads.

@ayaanahmad1085

Жыл бұрын

use adblock

I think you made an error ma'am. Converse : IF I don't go to town, THEN it is raining. and not ; IF I don't go to town, THEN it is not raining.

@SawFinMath

4 жыл бұрын

Spicos Flux That is what I said in the video...

@spicosflux9576

4 жыл бұрын

@@SawFinMath Not really ma'am. Perhaps it slipped your tongue.

@GokdenizOzkan

4 жыл бұрын

@@spicosflux9576 she says correct, actually. Maybe you misheard it? ;-;

@nadiakokoyev

3 жыл бұрын

I think he is right. At 8:26

@foresttrump

3 жыл бұрын

Hes right actually, slight slip of tongue i guess, put a comment in the video to let students know