Very informative course really appreciate that you are working towards educating people for free. ALWAYS, think that you have made huge impact on me and others students like me. I thought I am at level 0 of learning Discrete Structure, but I feel I am wrong since I know your channel I feel that I am at level 1 of learning Discrete Math 1.
This is much better than learning in my class. It was really easier to understand when you explained everything and did not left out any minor detail that often math teacher will always left out. Thank you
Again really appreciate all the great explanation and detailed notes! Thank you for being such a great teacher and sharing all these resources for free!
Thanks for sharing this on youtube! The video is very compact in information, and I actually like it better than my own teacher. My teacher spent 2-3 hours explaining a single section, and the videos only take less than 60 mins per section. This video really helps me out :)
You've made this so damn easy, when the practice example came at the end of this video I paused the video and knew how to do breakdown the compound propositions. I discovered your UA-cam Channel from a few reddit posts. Thank you for the help this semester virtually lol!
Greetings, you really give lectures and explainations perfectly i moved to another country and i can't learn DS in class and i have mid term exam in 10 days with this videos i learned alot and i hope you have all videos related to DS first semester love your videos
this is late but I liked the font style you used in the first 2 lessons, made it feel like I was reading from my notes! but these videos have really been helping me, thank you so much
in the example at 1:50, I'm confuse how the order of operation works, there was OR, if-then, and negation and in the order of operation table it says negation is 1, OR is 3rd, and if-then is 5th, why start at the 3rd one which is OR
I'm very confused by your example at 2:00. Firstly, according to what you mentioned earlier, the 'not' symbol goes first in the order of operations. And secondly, even if parenthesis actually goes first and simply was missing in the chart you showed in the earlier slide, then still in this case the "not r" should have gone first, since as you mention, you deliberately did not put parenthesis here. so clearly in this case the "not r" should have gone before the "p or q", no?
No. These are two separate concepts. This is about finding all of the possible outcomes of a proposition. So we begin with each proposition. Then each operation on a proposition, like negation, conjunction,etc.
This is explained in the textbook that goes along with these lectures. Here is the section dedicated to "Precedence of Logical Operators": We can construct compound propositions using the negation operator and the logical operators defined so far. We will generally use parentheses to specify the order in which logical operators in a compound proposition are to be applied. For instance, (p ∨ q) ∧ (¬r) is the conjunction of p ∨ q and ¬r. However, to reduce the number of parentheses, we specify that the negation operator is applied before all other logical operators. This means that ¬p ∧ q is the conjunction of ¬p and q, namely, (¬p) ∧ q, not the negation of the conjunction of p and q, namely ¬(p ∧ q). Another general rule of precedence is that the conjunction operator takes precedence over the disjunction operator, so that p ∧ q ∨ r means (p ∧ q) ∨ r rather than p ∧ (q ∨ r). Because this rule may be difficult to remember, we will continue to use parentheses so that the order of the disjunction and conjunction operators is clear. so basically you can construct a truth table however you like. order of operations is a different thing entirely.
First of all, a huge thank you for your channel. I have a question, how did you come up with the combinations for all 3 propositions? or in other words, is there a formula or something that I can follow to write combinations for 4 or 5 propositions? Thank you
@@SawFinMath Understood. I took discrete mathematics last year for grad school and was not aware of the prerequisites. I will look at your calculus videos.
Hello, I love your teaching and I know get to understand discrete maths, however I have one question? how do you know how many columns you have to make in a truth table coz I am still having a difficulty with that.
The number of columns should be two to account for the truth value of each proposition (one for true and one for false) on the left side. In the middle, we make a column for any compound proposition that makes up your final statements. On the right should be the final statement (or statements if you are trying to prove that two statements are equivalent).
@@SawFinMath thank you so much...I actually did those practice exercise and it helped a lot to understand more bout the columns.....would you kindly tell me also about the rows, how many truth of false should you write on the left side where you have your two first propositions? sorry for the many questions:) and thanks in advance
It is called vacuously true. Our implication says nothing about if the hypothesis is false. So 'if I overslept, then I will miss my morning class'. But then you don't oversleep. What does that mean about your morning class? Not a darn thing. So if the hypothesis is false, we call the statement vacuously true.
To be honest you are the best but not every student is genius 😂😂 I don't even know what compound proposition is so till I understand that am gonna stop this video at 1:20
these orders. well, i just dont see everyone or really people invested giving a solid look into how this good be used to create influential data so sad really. this could be universally useful
Very informative course really appreciate that you are working towards educating people for free. ALWAYS, think that you have made huge impact on me and others students like me. I thought I am at level 0 of learning Discrete Structure, but I feel I am wrong since I know your channel I feel that I am at level 1 of learning Discrete Math 1.
I'm so happy to hear this. Best of luck in your studies!
Best discrete teacher, i am zero level, i know your course
I appreciate it!
Got an exam coming up. You're a lifesaver
This is much better than learning in my class. It was really easier to understand when you explained everything and did not left out any minor detail that often math teacher will always left out. Thank you
Again really appreciate all the great explanation and detailed notes! Thank you for being such a great teacher and sharing all these resources for free!
So far they seem to be good set of lectures :)
Thank you!
A big thank you for making education accessible for everyone. You're amazing!
Thanks for sharing this on youtube! The video is very compact in information, and I actually like it better than my own teacher. My teacher spent 2-3 hours explaining a single section, and the videos only take less than 60 mins per section. This video really helps me out :)
hey Kim i just wanna say, i love you, you've saved my life in this course lol.
You've made this so damn easy, when the practice example came at the end of this video I paused the video and knew how to do breakdown the compound propositions. I discovered your UA-cam Channel from a few reddit posts. Thank you for the help this semester virtually lol!
Great explanation based on the testbook my school uses for teaching Discrete Math. Thank you so much!
Your videos are great. Thank you for the clear and easy to understand visuals and explanations.
Thank you so much for helping me cement my understanding of discrete maths concepts.
Greetings, you really give lectures and explainations perfectly i moved to another country and i can't learn DS in class and i have mid term exam in 10 days with this videos i learned alot and i hope you have all videos related to DS first semester love your videos
Thank you, Prof. Brehm, for great lessons.
Happy to help!
Ah I finnaly get it now! Breaking the steps down really helped me & now I can explain it really well.
Excellent Explanations ....Very Methodical......A BIG help
Thank You !!
This is the future! Thank you.
this channel needs to be promoted !!!
I know it. Too many irons on the fire to take the time to figure out how to do that. But I appreciate you watching!
this is late but I liked the font style you used in the first 2 lessons, made it feel like I was reading from my notes! but these videos have really been helping me, thank you so much
Fantastic course with a clear explanation and easy to understand!
I'm taking a discrete structure class this semester.
Thank you so much! Glad I could help!
Superb method of teaching ❤❤❤ I appreciate 🎉
in the example at 1:50, I'm confuse how the order of operation works, there was OR, if-then, and negation and in the order of operation table it says negation is 1, OR is 3rd, and if-then is 5th, why start at the 3rd one which is OR
Lol I hated discrete structures but I think I might pass the course just because of your lectures
Love how these lectures are presented and taught!
Massive appreciation , thank you very very much
11:10 how do we combine the values in the two compound columns to determine the final column?
Use the 4th ad 5th column in an "if then" implication to determine their truth values.
I understand it. I understand it now
So at the very end...does that mean that the compound proposition is equivalent to 'q' since "not q" is exactly the opposite of the solution?
I'm very confused by your example at 2:00. Firstly, according to what you mentioned earlier, the 'not' symbol goes first in the order of operations. And secondly, even if parenthesis actually goes first and simply was missing in the chart you showed in the earlier slide, then still in this case the "not r" should have gone first, since as you mention, you deliberately did not put parenthesis here. so clearly in this case the "not r" should have gone before the "p or q", no?
No. These are two separate concepts. This is about finding all of the possible outcomes of a proposition. So we begin with each proposition. Then each operation on a proposition, like negation, conjunction,etc.
@@SawFinMath Exactly, and since "not" comes before "or" in the order of operations, shouldn't "not r" come before "p or q" on the truth table?
Does that make a difference?
This is explained in the textbook that goes along with these lectures. Here is the section dedicated to "Precedence of Logical Operators":
We can construct compound propositions using the negation operator and the logical operators
defined so far. We will generally use parentheses to specify the order in which logical operators
in a compound proposition are to be applied. For instance, (p ∨ q) ∧ (¬r) is the conjunction
of p ∨ q and ¬r. However, to reduce the number of parentheses, we specify that the negation
operator is applied before all other logical operators. This means that ¬p ∧ q is the conjunction
of ¬p and q, namely, (¬p) ∧ q, not the negation of the conjunction of p and q, namely ¬(p ∧ q).
Another general rule of precedence is that the conjunction operator takes precedence over
the disjunction operator, so that p ∧ q ∨ r means (p ∧ q) ∨ r rather than p ∧ (q ∨ r). Because
this rule may be difficult to remember, we will continue to use parentheses so that the order of
the disjunction and conjunction operators is clear.
so basically you can construct a truth table however you like. order of operations is a different thing entirely.
awsome video, thank you very much
11:19 I don't get how is the end result False.
Excellent!! Thanx! 🎉 😊
Thank you very much!
First of all, a huge thank you for your channel. I have a question, how did you come up with the combinations for all 3 propositions? or in other words, is there a formula or something that I can follow to write combinations for 4 or 5 propositions? Thank you
thank you so much
What mathematics is required before learning discrete math?
@@jasonelliott729 For my university its pre-calculus along with another math course
We require calculus 1 and 2 before students can take discrete, more for mathematical maturity than for content.
@@SawFinMath Understood. I took discrete mathematics last year for grad school and was not aware of the prerequisites. I will look at your calculus videos.
Thank you lady
Hello, I love your teaching and I know get to understand discrete maths, however I have one question? how do you know how many columns you have to make in a truth table coz I am still having a difficulty with that.
The number of columns should be two to account for the truth value of each proposition (one for true and one for false) on the left side. In the middle, we make a column for any compound proposition that makes up your final statements. On the right should be the final statement (or statements if you are trying to prove that two statements are equivalent).
@@SawFinMath thank you so much...I actually did those practice exercise and it helped a lot to understand more bout the columns.....would you kindly tell me also about the rows, how many truth of false should you write on the left side where you have your two first propositions? sorry for the many questions:) and thanks in advance
Sure. There should be a heading row and then 2^n rows where n is the number of propositions
Even without drawing the truth table, if one can solve the equation (p v ~q) -> (p ^ q), it turns out to be q
super helpful
thanks so much
Really nice.
Thank you for the help holy
Thank you ma'am.
Most welcome 😊
completed!
Why does the hypothesis being false make the proposition true? This bit is never explained.
It is called vacuously true. Our implication says nothing about if the hypothesis is false. So 'if I overslept, then I will miss my morning class'. But then you don't oversleep. What does that mean about your morning class? Not a darn thing. So if the hypothesis is false, we call the statement vacuously true.
To be honest you are the best but not every student is genius 😂😂 I don't even know what compound proposition is so till I understand that am gonna stop this video at 1:20
thanks
You’re so adorable
these orders. well, i just dont see everyone or really people invested giving a solid look into how this good be used to create influential data so sad really. this could be universally useful
I'm not sure what you mean by this...