Your lectures are amaze-balls! Thank you, Professor Brehm. I'm not a math major (actually I don't even attend a college) but your explanations have me hooked. I'm interested in eventually learning more advanced logic and getting into hyperreal numbers and set theory. Thanks for making this information accessible to noobs like me :) -Float Circuit
8:20, be careful using "either or" because that could indicate Exclusive or (XOR). Other than that, thanks for this video! I have a midterm tomorrow and this helped me review!
@15:39 ∃m ∀a ∃f (P(m, f) ∧ Q(f, a) ), can we switch order of ∀a and ∃f and put it as ∃m ∃f ∀a (P(m, f) ∧ Q(f, a) ) in this case? (I am aware that ∀x ∃y and ∃y ∀x are not the same in most cases, but in this specific case, does it make any difference if we switch order of ∀a and ∃f?) Thanks!
For the example at 13:55, why couldn't we have let P(x,y) denote that x has flown on airline y? Why do we have to split it into two different predicates?
You could certainly write it another way, however, you must be careful. If you use P(x, y) then how will you specify that the man has taken at least one flight on EVERY airline, as opposed to taken EVERY flight on every airline. That is why I separated.
@@jamesb101100 This would be incorrect. There exists a man such that for all flights the man has taken the flight. THis doesn't reference airlines. Also, you can't use x=man.
I'm a bit confused at 6:30 for part B. With the implication, if x were to equal y, then the implication would come out true (because false -> ___ always equals true). Shouldn't it come out false if x and y are equal? Also, there exists an x where all y's don't equal isn't true so that confuses me too. It made sense verbally to me, but when I try to work it out logically it confuses me...
I am saying that x is not equal to y, implying that x and y are different students. For all students y (meaning all other students in the class besides x), student x has not received a text or email.
I'm a bit confused at 6:00, in the beginning of the question it specifies that E (x,y) denotes that "x sent y an email" however in the answer it reads out that: "there exists an x such that all y's etc" when I thought it would instead be "there exists a y such that all x's etc" because the student in the class is the only person who did not receive anything not the only person who did not send anything. Can you please explain this to me a little more in detail? And thank you for this playlist btw it is really helping me out cuz i cannot understand my prof for the life of me XD
Check out the new playlist. th-cam.com/play/PLl-gb0E4MII28GykmtuBXNUNoej-vY5Rz.html I make the question you are referring to more clear. It has to do with DeMorgan's Law.
Around 12:18 I dont agree with how x and y were first presented being in the universes of student and class (respectively) at first and then x and y both became students for the sentence below it.
It is OK to do that, since when I defined the proposition, I specified S(x, y), meaning the first variable gives the student and the second gives the class. If you will notice, I used z as the class that both students are enrolled in since for both students x and y (who are not equal) I used class z.
11:15 S(x,y) denotes "student x has taken class y" then how did "y" become a student and z became a class? when it denoted "y is a class" and z was never denoted on the statement??(Thanks for the videos ive been watching all of it it helps me alot)
Check out the new playlist. th-cam.com/play/PLl-gb0E4MII28GykmtuBXNUNoej-vY5Rz.html I had several questions about that one. Essentially we define the first value as the student and the second value as the class. So it doesn't matter which variable I use. I could have student S(a, b) and it would be the same.
When we define a propositional function like P(x, y) means x took y class, we can still then say P(a, b), which would mean a took b class. It doesn't have to be x or y or z.
what if we did not change the order of E(x,y) in 6.30 and instead of that write : for some X all Y beginning of the question since x is the sender and y is the receiver? thank you for your effort btw.
We couldn't just switch x and y since we are saying that there exists a student who didn't receive a text or email. In order to switch x and y on the right side of our statement, we would have to switch them at the beginning, as well. We would say that there exists some y that for all x, then x and y could be written correctly at the end of the statement.
Your lectures are amaze-balls! Thank you, Professor Brehm. I'm not a math major (actually I don't even attend a college) but your explanations have me hooked. I'm interested in eventually learning more advanced logic and getting into hyperreal numbers and set theory. Thanks for making this information accessible to noobs like me :)
-Float Circuit
So glad I could help :) (and yes I am WAY behind on responding to comments!)
@@SawFinMath Haha it's all good, and happy 2021 to you!
Got a midterm tomorrow morning and this helped me understand translating predicates so much better, thank you!
iam watching you instead of attending my actual lecture and iam not sorry about it. thanks for great content!
Project Hu148 By far my favorite comment on one of my videos :)
@@SawFinMath anytime :)
8:20, be careful using "either or" because that could indicate Exclusive or (XOR). Other than that, thanks for this video! I have a midterm tomorrow and this helped me review!
@15:39 ∃m ∀a ∃f (P(m, f) ∧ Q(f, a) ), can we switch order of ∀a and ∃f and put it as ∃m ∃f ∀a (P(m, f) ∧ Q(f, a) ) in this case? (I am aware that ∀x ∃y and ∃y ∀x are not the same in most cases, but in this specific case, does it make any difference if we switch order of ∀a and ∃f?) Thanks!
Been using these videos to study for midterm :D
Hope you ace it! But be sure to check out the new playlist.
at 6:30 b. , shouldn't the conjunction symbol be disjuction V , since it is "has not received a text or email"
Mam Thanks A Lot . My Life Just got a lot easier .
For the example at 13:55, why couldn't we have let P(x,y) denote that x has flown on airline y? Why do we have to split it into two different predicates?
I'm also confused about that.
I got P(x,y): "x has taken flight y"
E(x)∀y (x=man ^ P(x,y))
wouldn't this also be correct?
You could certainly write it another way, however, you must be careful. If you use P(x, y) then how will you specify that the man has taken at least one flight on EVERY airline, as opposed to taken EVERY flight on every airline. That is why I separated.
@@jamesb101100 This would be incorrect. There exists a man such that for all flights the man has taken the flight. THis doesn't reference airlines. Also, you can't use x=man.
I think there's a mistake in 6:00. It should be a "but" between the statement E and statement T instead of a "and".
I'm a bit confused at 6:30 for part B.
With the implication, if x were to equal y, then the implication would come out true (because false -> ___ always equals true). Shouldn't it come out false if x and y are equal? Also, there exists an x where all y's don't equal isn't true so that confuses me too. It made sense verbally to me, but when I try to work it out logically it confuses me...
I am saying that x is not equal to y, implying that x and y are different students. For all students y (meaning all other students in the class besides x), student x has not received a text or email.
I'm a bit confused at 6:00, in the beginning of the question it specifies that E (x,y) denotes that "x sent y an email" however in the answer it reads out that: "there exists an x such that all y's etc" when I thought it would instead be "there exists a y such that all x's etc" because the student in the class is the only person who did not receive anything not the only person who did not send anything. Can you please explain this to me a little more in detail? And thank you for this playlist btw it is really helping me out cuz i cannot understand my prof for the life of me XD
Great series! but I think that's a very unfortunate use of 'either' at 9:00, especially how non-intuitive some people find inclusive or
When to use => and when to use *?
good shit familiy. GANG GANG
You just earned a subscriber :)
Awesome!
5:57 Shouldnt that be a disjunction not conjunction since its a text "or" email (Thanks for the videos ive been watching all of it it helps me alot)
Check out the new playlist. th-cam.com/play/PLl-gb0E4MII28GykmtuBXNUNoej-vY5Rz.html I make the question you are referring to more clear. It has to do with DeMorgan's Law.
Around 12:18 I dont agree with how x and y were first presented being in the universes of student and class (respectively) at first and then x and y both became students for the sentence below it.
It is OK to do that, since when I defined the proposition, I specified S(x, y), meaning the first variable gives the student and the second gives the class. If you will notice, I used z as the class that both students are enrolled in since for both students x and y (who are not equal) I used class z.
11:15 S(x,y) denotes "student x has taken class y" then how did "y" become a student and z became a class? when it denoted "y is a class" and z was never denoted on the statement??(Thanks for the videos ive been watching all of it it helps me alot)
Check out the new playlist. th-cam.com/play/PLl-gb0E4MII28GykmtuBXNUNoej-vY5Rz.html I had several questions about that one. Essentially we define the first value as the student and the second value as the class. So it doesn't matter which variable I use. I could have student S(a, b) and it would be the same.
thankyouuuu very much !
thank you
Why is y a student and not a class at 12:00 ?
This makes no sense to me. y is defined as a class, not a student, and z is never defined as to what it is.
When we define a propositional function like P(x, y) means x took y class, we can still then say P(a, b), which would mean a took b class. It doesn't have to be x or y or z.
Strange when you had "BU" on the video. I don't go to your BU (Bellevue) but I do go to a BU (Boston U).
Mam Please Help me translate this Question : Someone loves everyone besides himself or herself
what if we did not change the order of E(x,y) in 6.30 and instead of that write : for some X all Y beginning of the question since x is the sender and y is the receiver? thank you for your effort btw.
We couldn't just switch x and y since we are saying that there exists a student who didn't receive a text or email. In order to switch x and y on the right side of our statement, we would have to switch them at the beginning, as well. We would say that there exists some y that for all x, then x and y could be written correctly at the end of the statement.
@@SawFinMath thank you so much , it all makes sense now.
This video is lit! #gang gang
never thought i'd ask this but, home work????
I stopped putting the homework in the videos.
1.5: P.64-67(3, 6, 9, 10, 15, 17, 20, 21)
it's more confusing than my professor's teaching
Sorry I couldn't help.
There is a man who*, haha
marry me.
Thanks for the offer :) You should switch over to the new playlist if you're learning Discrete Math.
This makes no sense to me. y is defined as a class, not a student, and z is never defined as to what it is.