[Discrete Mathematics] Sheffer Stroke Examples
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- เผยแพร่เมื่อ 18 พ.ค. 2016
- We introduce the sheffer stroke and do some examples.
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yes! now I know how to covert and/or gates into NAND gates!
For the first example can you not do this ~(~p n ~q) so answer will be same as the secound ?
My brain is hanging on by a thread lol
5:16 instead of (p↑p) ↑ (q↑q) could you have used (¬p ↑ ¬q) as you are using the sheffer stroke here too? and also at 3:56, you already used the sheffer stoke at ¬(p↑q) so why go even further to show it as (p↑q) ↑ (p↑q)?
Yeah i got (¬p ↑ ¬q) as well when i was trying to work out my own definition.
I think the idea here is to be able to write any logical expression using ONLY the Sheffer stroke.
Wouldn't it be sufficient to say that (p v q) (~p nand ~q) ?
Why was it necessary to turn ~p and ~q into (p nand p) and (q nand q) ?
@JojoMojo225 Is it possible to find a different soloution than that of TrevTutor still using only 'nand'?
(p and q) is not equivalent to (p up q) up (p up q), only if you negate it or do i misunderstand something?
Two years late but for anybody with a similar question.
P UP Q is the same as taking an AND and NOTTING it. Within the second UP since (P UP Q) is both terms in the UP it'll just act as a NOT. Therefore inversing it giving us our AND.
P | Q | P UP Q | (P UP Q) UP (P UP Q) | P AND Q |
1 | 1 | 0 | 1 | 1 |
1 | 0 | 1 | 0 | 0 |
0 | 1 | 1 | 0 | 0 |
0 | 0 | 1 | 0 | 0 |
Don't quiet understand the end part of pvq part ??? Is it simple because ¬ (negation) is outside the bracket ¬(____) whilst the and connective is inside the bracket i.e -> ¬(__(and)__) . Is that a general rule ??? Confused ??
Yeah, it's a "general" rule, but you can prove it yourself using truth tables. It's a DeMorgan's law transformation where ~(P ^ Q) ~P v ~Q. In this case he's going the other way and there's an extra "~" :
~~P v ~~Q ~(~P ^ ~Q)
He touched on it about...two lessons ago?
The most useful of this feature is in circuit manufacture, you only build nand circuit for all kinds of circuit.
2:37
0:00
de morgan ruleess...(but not presented yet)
It is this
2:45 How did this become not not p and q? = ( I'm lost
At 4:45 how???
not p and not q ~ not(p and q) ????????
It's an analogy in a sense. I'm saying it's of the form ~(p ^ q), so we can use our rule for ~(p ^ q), then apply rules to ~p and ~q on the inside to get a result for ~(~p ^ ~q)
Sorry, but I'm lost at 4:30 how is that possible?
I did not understand that either, the change from an 'or' to 'and' operator?
Using DeMorgan's Law, explained in the next video on this playlist.
i didn't understand how: ~~p or ~~q became ~(~p and ~q).
"~p v ~q" means that you don't have both "p" and "q" (at least one of them is negated), that is "~(p & q)"; now the example says: "~~p v ~~q" This means that you don't have both "~p" and "~q" (at least one of them is negated), that is "~(~p & ~q)".
This equivalence of statement forms ~(p & q) ↔️ (~p v ~q) is one of the two called De Morgan's Laws / Theorems / Rules. They can be proven with truth tables or by derivation.
@@materialknight thx dude i was also stuck at that part
i think 'v' is or not and
en.wikipedia.org/wiki/De_Morgan%27s_laws
¬(p ∨ q) = (¬p ∧ ¬q)
ergo
(p ∨ q) = ¬(¬p ∧ ¬q)
Too bad, he doesn't teach anymore
He did not give a definition of the Sheffer stroke, just introduced it via equivalence
Could kinda follow this after watching 3 times, but I don't understand the purpose of any of it.
Just more arbitrary cryptic syntax and rules/tricks to memorize for a test before brain dumping everything.
This is why people hate math. Ugh - gonna fail my damn class.
completely uselss stuff lol