Discrete Math - 1.6.1 Rules of Inference for Propositional Logic
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- čas přidán 30. 07. 2024
- Building a valid argument using rules of inference for propositions.
Video Chapters:
Introduction 0:00
A Valid Argument 0:07
Modus Ponens and Modus Tollens 3:08
Hypothetical Syllogism and Disjunctive Syllogism 6:01
Addition and Simplification 7:56
Conjunction and Resolution 9:39
Build a Valid Argument Using Premise 12:10
Practice with Me (Assign Propositions) 16:40
Practice with Me (Challenging) 21:45
Up Next 28:19
Textbook: Rosen, Discrete Mathematics and Its Applications, 7e
Playlist: • Discrete Math I (Entir...
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The challenging example was exactly what I was looking for in order to understand more complicated arguments. Thank you so much, these are fun!
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So happy I could help!
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Thank you, Kimberly, for your videos. I finally understood deductive thinking (going from universal to particular: particular being necessarily true when the said particular belongs to the group of the universal), premise, logical symbols etc. thanks to your videos. I also read an article on inductive and deductive thinking on Wikipedia, and inductive thinking clicked as well. The definition on Wikipedia was horrible, but I got that inductive thinking is the opposite of deductive thinking i.e. Going from the particular instance(s) to universal. I also understood that inductive conclusions can never be true but their likelihood of being true can be increased. However even a single instance to the contrary of the conclusion leads to a revision of the conclusion (ideally).
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Glad it helped!
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I got my graduate degree from UNO! I had some great professors and a not-so-great one. Glad I could help!
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Thank you so much for your great explanations. DM really starts making fun. I wish all my professors could explain Math that way !
True
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You are so great, I hope I had you as a professor. And just a suggestion in the practice from 16:41 to 21:41, we could have also used hypothetical syllogism to prove the conclusion:) Thanks!
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I would like to ask on your last example, isn't the disjunctive syllabus r v s and not s suppose to give s instead or r?
Resolution:
Just remember p->q has same truth table with ~p or q
so, if ~p or r is same as p->r. Therefore we can replace p with r in p or q, which is same as r or q.
These are saving me for my midterm thank you
You are welcome!
What do you do if you have 4 variables? How can I identify the type of Inferences if there are 4 letters ex; Q,p,r ,s
thank you so much!
I am a Computer Systems Major - Upper Senior at City Tech. This slides are helping me in advance. Class is online - Spring 2022 but will be on campus once a month. I hope to get an A in MAT 2440. I will also take MAT 2540 in Fall 2020. Thank you very much for posting these videos.
Glad I could help!
Just to make sure I got this right: An argument is the CLAIM that (p1 and p2 and ... pN) imply q. A VALID argument is an argument for that this claim holds. Is that correct?
Best teacher to date
Trying to self study here. Just curious, if I have p -> q and not p. Then is the result inconclusive?
Why is it modus ponens in the 3rd step of the last example?
@15:38, how does she use simplification for the second one?
for the second example, can we use hypothetical syllogism? p-> not q, -q implies not r, therefore p implies r, then using modus ponens since p is true so is r?
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So glad I could help!
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Good day maam Kimberly!
regarding in disjunctive Syllogism,
is (( p v q ) ^ ~ p) --> q = ((p v q) ^ ~q) --> p?
Help professor,
I am precisely asking what does the definition of even numbers refers to.Or for simply,the
definitions of chairs,tables,spoons
etc refers to a class satisfying the stated property or these terms symbolise any object satisfying stated property.
At 15:56, is it ok if I did Modus Ponens first and then simplification to reach the same conclusion?
hi L
Lots of love from India
If you don't have "q" as a premise. How would you solve this?
Well explained
I was confused about your last example. Why does leaving r at the end imply that p->r
The first step was q. Using the steps we arrive at r. So q implies r.
I wanna ask a dumb question. Does (q v p) ^ ( h v k) -> q v p true?
It would be nice if there were more middle level sample questions about Rules of Inference.
Hi Kimberly, I'm a bit confused about the topic of this video intersects with section 1.3.3 (Constructing New Logical Equivalences) . Wasn't that constructing proofs as well? thanks for all the great videos.
This is late but for any newcomers 1.3.3 dealt with making two propositions equal, while this video deals with proving that a proposition is true (a tautology)
Can someone explain how to get the 3rd step which takes place around 15:10?
Why can't you just write q instead of p implies q?
You have to have a reason for every step. I can't just say "q" without a logical equivalence. So I have to state the rules I am using. In this case, that is simplification and modus ponens.
I think the video unfortunately is slightly open for misinterpretation in this exact segment unless you observe quite carefully. It also took me a while to understand what was being done.
So the rule of simplification that is used was explained in general by p and q as variable names, which unfortunately also were the specific variable names of the logical statement we investigated. So lets instead explain the simplification rule by using myVar1 and myVar2: From the knowledge that myVar1 AND myVar2 is true, we can infer that myVar1 is true (and equivalently that myVar2 is true). Now to take this general simplification rule and apply it to the example, we would recognize myVar1 as p, and myVar2 as "If p then q". Now it must be since that the premise states that p AND (if p then q) is true, it also follows that both p is true, and (if p then q) is true.
For the disjunction rule, you took the r.
But, according to the formula, u should take the s to be true!?
(p or q) and not q then q
you did
(p or q) and not q then p.
Are they interchangeable ??
Kinda confused rn!!
Thank you!!! i have a small question, do we have to memorize all of the rules?
I would just keep a list handy for easy reference
Queen
👸
Much ove.
Love*
16:35
7:25 kinda need clarification
Not sure what you mean.
21:52
Can we just say:
1. u→p
q→(u∧t)
∴ q→(p∧t)
2. ¬s
(p∧t)→(r∨s)
∴ (p∧t)→r
3. q→(p∧t)
(p∧t)→r
∴ q→r
I think I'm too stupid to understand this.
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I find that this course video is different and in a different order then my book is. Which mean's if I want to use this to learn I need to finish all 80 videos in 1 to 2 weeks lol cry
Or....compare your topic list to the topic list in the book I used. Then watch the videos in the order of your text
@@SawFinMath Thank You for answering my response. I am just saying but 1.6.1 to 1.8.2 is hard to follow. I am currently on 2.1.1
The college that I am taking is the class "Discreet Math" is know as "Discreet Structures" part of the Computer Science path and the class is called CSC 7 at Riverside City College. They use the discrete mathematics and its applications by susanna 4th.
hello can anyone help me with this one?
Premises: (¬p → ¬q),(r → p),(¬r → q) conclusion p
Sure, by contraposition law, from (¬p → ¬q) we derive (q → p).
Now from (¬r → q) and (q → p) we derive that (¬r → p) by hypothetical syllogism.
Now we know that (r → p) and (¬r → p).
The last step is the disjunction elimination rule: all we need to invoke is the law of excluded middle (r ∨ ¬r), so (p) follows.
Who came here few days before algebra exam 😭
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This doesn’t make any sense
Remembering the names for those operations will definitely kill me. Hypothetical syllogwhatnow? Amazing videos nonetheless of course!
Thank u for these good lesson
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Glad to hear that