LOL, it wasn't my problem of, my problem how to disprove that a specific function isn't a complete set at all? isn't there any other quick steps for verifying it's a complete set or not?


and lets say I have an operators {XOR,NAND} and asking me if it's a complete set or not? how would I even get started? can you solve it for me to know just how the things go behind of this logic?

Can you show that NAND is a complete set by itself?

If so, then any set that either contains a NAND or can implement a NAND is a complete set. Similarly, any set that either contains a NOR or can implement a NOR is a complete set.

 

Can you show that NAND is a complete set by itself?

If so, then any set that either contains a NAND or can implement a NAND is a complete set. Similarly, any set that either contains a NOR or can implement a NOR is a complete set.

Aha got the idea...and I proved that thanks!!!

But now I'm struggling for proving that {XOR,AND} isn't a complete set? from my understanding it's not but how to prove that by logical way? isn't there any possible way of?

 

Aha got the idea...and I proved that thanks!!!

But now I'm struggling for proving that {XOR,AND} isn't a complete set? from my understanding it's not but how to prove that by logical way? isn't there any possible way of?

You know that if you can implement both NOT and AND that you have a complete set. Clearly implementing AND is trivial. Are you SURE that you can't use those two gates to implement a NOT function?

 

You know that if you can implement both NOT and AND that you have a complete set. Clearly implementing AND is trivial. Are you SURE that you can't use those two gates to implement a NOT function?

I really know that but is that enough for disproving that function isn't a set complement?
I'm meaning is that a completely correct to write like this answer to this question? wouldn't be any implement of digital logic way to prove that it's not a set complete..?

 

For example, I've read if the function isn't returning to you "1" for all its conditions then it wouldn't be a set complete anymore.

 

Are you working in a particular environment or system?
Max.

 

Are you working in a particular environment or system?
Max.

Lol no its a homework question-nothing else lmfau!

 

For example, I've read if the function isn't returning to you "1" for all its conditions then it wouldn't be a set complete anymore.

I'm not following this at all. What's "the function" you are talking about?

 

I really know that but is that enough for disproving that function isn't a set complement?
I'm meaning is that a completely correct to write like this answer to this question? wouldn't be any implement of digital logic way to prove that it's not a set complete..?

If the claim is that a pot can't hold two gallons of water and I prove that it can hold two gallons of water, doesn't that disprove the claim that it can't hold two gallons of water?

If you prove that a set is complete, then doesn't that disprove any claim that it is not complete?

I can't tell how to parse your last question. Please try to restate it.

 

If the claim is that a pot can't hold two gallons of water and I prove that it can hold two gallons of water, doesn't that disprove the claim that it can't hold two gallons of water?

If you prove that a set is complete, then doesn't that disprove any claim that it is not complete?

I can't tell how to parse your last question. Please try to restate it.

it does!

 

Excuse me, what about circuit "AND"? isn't it a complete system process?
I'm asking because I can for example gets from AND the circuit "NOT" , then "And" itself I already have and "NOT" is stem from it, which {AND,NOT} is a group of a complete system, then I can assume that "AND" is a complete system, am I right?
e.g:
inputs, (x)' * (x)'=(x)' I got the "NOT" by using "AND"..
and about AND itself X*Y is already given, then I got group {NOT,AND} which that's group of a complete process system...

Any clue if I'm talking right or not?

Another note,
if I succeeded to get from a given circuit another boolean circuit, can I use this another boolean circuit while parsing to prove other systems?
to be more simple:
for example, if there's a given circuit "OR" and telling me to prove that's a complete set system, then I can simply extract from OR, the circuit NOT by (X)'+(X)'=X' then regarding to what I'm saying in my note, I can now use the circuit "NOT" and the given circuit "OR", then I can for example do (x'+y')'=x*y...I got "AND"'s circuit....if this things go so, most circuits I can assume it's a complete set system...so I think I'm talking wrong and I need a help to correct me in the right direction.


thanks in advance.

 

Excuse me, what about circuit "AND"? isn't it a complete system process?
I'm asking because I can for example gets from AND the circuit "NOT" , then "And" itself I already have and "NOT" is stem from it, which {AND,NOT} is a group of a complete system, then I can assume that "AND" is a complete system, am I right?
e.g:
inputs, (x)' * (x)'=(x)' I got the "NOT" by using "AND"..
and about AND itself X*Y is already given, then I got group {NOT,AND} which that's group of a complete process system...

Any clue if I'm talking right or not?

Another note,
if I succeeded to get from a given circuit another boolean circuit, can I use this another boolean circuit while parsing to prove other systems?
to be more simple:
for example, if there's a given circuit "OR" and telling me to prove that's a complete set system, then I can simply extract from OR, the circuit NOT by (X)'+(X)'=X' then regarding to what I'm saying in my note, I can now use the circuit "NOT" and the given circuit "OR", then I can for example do (x'+y')'=x*y...I got "AND"'s circuit....if this things go so, most circuits I can assume it's a complete set system...so I think I'm talking wrong and I need a help to correct me in the right direction.


thanks in advance.

First you need to show how you get NOT from just AND gates. If you can do that, then clearly you can make a NAND gate and since we already know that NAND is a Universal Gate, you are done.

But getting a NOT from just AND gates is going to be challenging.

 

Not challenging at all, I can do like (x)' * (x)'=x' then I got the circuit NOT! so..?
I used here circuit "AND" and got the circuit not! ..

but what I guess is I shouldn't use from the beginning the circuit NOT in (X)' right?

 

Not challenging at all, I can do like (x)' * (x)'=x' then I got the circuit NOT! so..?

So.... you used both the NOT and the AND functions to get your NOT.

In order to show that you can make a NOT gate from nothing but AND gates, you have to use NOTHING but AND gates. So your expression can ONLY have * operators and CANNOT have ANY ' operators.

I used here circuit "AND" and got the circuit not! ..

No, you used one AND gate and two NOT gates. Where did the two NOT gates from from?

but what I guess is I shouldn't use from the beginning the circuit NOT in (X)' right?

Right!