Natural Deduction Proofs: practise examples | Attic Philosophy
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- เผยแพร่เมื่อ 9 ก.ค. 2024
- How do Natural Deduction proofs work in logic? In this video, I show you how it works by going through some example proofs. This is part of a series of videos introducing the basics of logic. If there’s topics you’d like covered, leave me a comment below!
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00:00 intro
00:42 recap of the rules
01:10 example 1
03:57 example 2
05:25 Proof Strategy
08:31 example 3
10:41 proving equivalence
11:21 example 4
14:21 example 5: de Morgan equivalence
16:46 important logical equivalences
17:22 wrap up
More on natural deduction:
Proofs in Logic: • How to do Natural Dedu...
Natural Deduction: • How to do Natural Dedu...
Rules for Natural Deduction proofs: • Rules for Natural Dedu...
Links:
My academic philosophy page: markjago.net
My book What Truth Is: bit.ly/JagoTruth
Most of my publications are available freely here: philpapers.org/s/Mark%20Jago
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#logic #proof #naturaldeduction
How has this guy only 2.61k subs this is A+++++++++++ level teaching skills thanks so much I will post how my exam tomorrow went
Thanks, hope the exam went well!
@@AtticPhilosophy yes I think I nailed it thanks man
how are you doing now in life?@@sjoerdv800
I was honestly stranded cause I didn't get how my teacher explained it and I have a test tomorrow you really helped me thank you
and I would love to see you post again even if I'm new to this channel thank you
That little bit of strategy completely unlocked all of natural deduction for me, thanks!
Fantastic, glad it helped!
I couldn't figure this out until I watched your video, thank you!
thank you so much, without you, I could never understand the natural deduction
Amazing video! Thank you so much for explaining even the tiniest details, it helped my understanding a lot!
Thanks! Glad it helped.
Hello Sir ! Your videos are absolutely wonderful. They're both short and extremely complete + very easy to understand. Thanks a lot for your hard work !
You’re welcome!
Thanks so much for making this video! :) It helped a lot where my lecturer didn't give great examples or explain them well as he went through
You're very welcome!
you taught me in less than 20 minutes what my prof failed do whole semester.cheers
Thanks - glad it helped!
Excellent explanations. THANK YOU!
Thank you!
I love how he explains it
YOU MY MATE !!! YOU JUST MADE MY LIFE WAY EASIER!! IF I WERE NEXT TO YOU RIGHT NOW, I WOULD GIVE YOU A BIG HUG!!! THIS WAS THE TOPIC MY PROFF COULDNT EXPLAİN PROPERLY FOR 2.5 HOURS! APPRECIATE THAT VIDEO!!!!
Great, glad it helped!
Hope you get a lot of subs soon! Thank you for great content.
Thanks!
Now I'm teaching logic, this is SOOO helpful!!! thanks so much!
Good for you! How's it going? If you share with you students, let me know what they think.
@@AtticPhilosophy they had a bit of a hard time, but is becuase mexican universities don't teach logic like in Europe, but I had some students that did really good because they understood the examples (the suppose b, use a conclude c was sooo good! ). I am really greatful for your videos! it made me understand it better so I could teach it ^^ particulary cause as a student this was really hard for me!
you are a legend
coming in clutch ty
Great! Glad it helped.
thanks, you will save my logic exam!
Great! Hope it goes well.
bro u drop that👑
Thanks!
this is my favourite tutorial video on TH-cam. not my first comment here!
Wow, thanks!
I love you man
Great video, not many videos show proper sub-proofs
Thanks!
Goat 🐐
Using the above process, we are able to prove left side from right hand side and vice versa.
But if question says to prove the validity by natural deduction, and we have an expression. then how do we proceed with it ? we don't have any right hand side or left hand side in that case.
A question in my paper has come like:
Prove by natural deduction the validty of:
(P ->Q) -> (P -> ( P ^ Q))
Please help.
If you need to prove a sentence (ie with no premises), look at its main connective, and use that intro rule. So in this case, use -> intro, by assuming p->a and reasoning to p->(p&q). Good luck!
Your channel is a hidden gem, I absolutely love your channel
question:
Is
A \turnstile B
equivalent to
\turnstile A --> B
?
I suppose I should try and prove it using equivalences! my bad
Thanks! Yes, they’re equivalent (in most logics). If you can prove B from A (A l- B) then you can assume A, derive B, and so infer |- A -> B, and vice versa.
my exam is on this Monday. Can you please solve my query:
for example 4, when we were proving from right side to left side, how did you introduce ~B from A ? what rule is that ?
You assume A & ~B, and from that, infer A on its own, and then ~B on its own. (So ~B comes from A&~B, not from A). Good luck!
thank you so much sir
I was struggling in it until I found your video...but now I'm not !
Fantastic, glad it helped!
Heyy thanks for the video. I was just trying to prove the tautologies at the end of the video and came across a problem with one of DeMorgan laws. That one of ~(A ^ B) -| |- ~A v ~B. I can't figure how to start the proof that assumes ~(A ^ B) and concludes ~A v ~B. I have no problem with a proof for ~~(A ^ B) -| |- ~(~A v ~B) since I can use double negation and do a lot more with A ^ B. But comming up with something for ~(A ^ B) is a bit tricky for me
For this one, you can’t prove ~A and can’t prove ~B, so you can’t use v-intro. The only other option is indirect proof, from assuming ~(~A v ~B). Try that, then you have 2 premises to get a contradiction from.
@@AtticPhilosophy Ah ok. So given ~(~A v ~B), i think A could be inferred, then B, then A ^ B and get the contradiction with the initial hypothesis ~(A ^ B). Guess that's it. Thanks!
@@gonzajuarez4918 That's it. You need to make extra assumptions along the way (different ways to do this - experiment!) It's a very indirect proof and, incidentally, not intuitionistically valid (since you *have* to use indirect proof).
examples speak louder than words. idk just feels right
Thanks!
How would you breakdown the following formula? ~W • ~~Z, (~W • X) → Y, ~Z v X, therefore Y My logic class is kicking my butt. The truth tables were fun but this part not so much. Sigh....
That one's quite tough! Assuming . means 'and' (&) here. So from ~W & ~~Z you get ~W, ~~Z, and Z. Use v-elim on ~Z v X gets you X (you work out the steps involved). That gets you to ~W & X, you can finish it from there!
practice is the noun and practise is the verb. I don't think you are respecting this distinction.
@@nitishgautam5728 it's its, not it's
@@feraudyh right , ...
Is this logic right? P = Practice is the noun , Q = Practice is the verb , but we know that Practice can be both noun and verb depending on sentence , this is called lexical ambiguity therefore .... It's not clear which practice we are talking about .
its really good, thanks but stop putting your face for 5 seconds every 1 minute
Thanks! So you'd like 10 seconds every minute? Weird.