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
Uhh ... the fact that this has been RECORDED, means, the lessons will be available, long after ALL of us are gone. Just as, kids today can enjoy Charlie Chaplin, Humphrey Bogart, and Shemp [of the Three Stooges] today, even though all of those artists [of which, Shemp was the best] were gone, long before many people today were even born. Just sayin'. [You're welcome.]
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 :)
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
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
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.
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.
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
