set theory. How will I answer

[shahar]

Let A,B are sets.
Given P(B) – P(A) = P(B) – {null}
Prove B – A = B

 

[shahar]

P(B) = Power set of B
P(A) = Power set of A
A and B are any kind of sets.

B - A = B means The set B without the elements of set B equal to... B

More question: (I think I needed to add it in the beginning: Can B would be A NULL Set?!

 

[Dr.Peterson]

Let A,B be sets.
Given P(B) – P(A) = P(B) – {null}
Prove B – A = B

I'll make corrections in the following:

P(B) = Power set of B
P(A) = Power set of A
A and B are any kind of sets.

B - A = B means The set B without the elements of set A equal to... B

More question: (I think I needed to add it in the beginning: Would A be a NULL Set?!

It certainly looks as if A must be null. But you have to prove it. How do you prove that two sets are equal?

Suppose that x is an element of B – A. Show that x is an element of B.
Suppose that x is an element of B. Show that x is an element of B - A.

Or, do you have any theorems that can apply?

 

[shahar]

I'll make corrections in the following:


It certainly looks as if A must be null. But you have to prove it. How do you prove that two sets are equal?

Suppose that x is an element of B – A. Show that x is an element of B.
Suppose that x is an element of B. Show that x is an element of B - A.

Or, do you have any theorems that can apply?

I know that this deals no with theorems.
But definitions.
I know that if A and B are equals A is subset of B and B is subset of A.
So How I continue from here?

 

[Dr.Peterson]

I know that this deals no with theorems.
But definitions.
I know that if A and B are equals A is subset of B and B is subset of A.
So How I continue from here?

Why did you choose not to take my advice? I showed you a way to start.

And after saying you would not use theorems, you stated a theorem! Possibly that could be of use if you have theorems about power sets of subsets, but I think my suggestion is probably easier.

 

[pka]

Let A,B are sets.
Given P(B) – P(A) = P(B) – {null}
Prove B – A = B

To shahar: If you are now planning to post set theory questions, then you should learn LaTeX coding.
The \(\mathscr{P}(B)\setminus\mathscr{P}(A)=\mathscr{P}(B)\setminus\{\emptyset\}\) distinguishes power-sets from probability of a set.
The above says that removing the subsets of \(A\) from the subsets of \(B\) leaves the non-empty subsets of \(B\).
That clearly means that \(A\cap B=\emptyset\).
If you click Reply you see the coding.

 

[shahar]

My name is Shahar with a capital S.
Now is becoming late for me. I look on it tomorrow. Thanks.

 

[Steven G]

In defense of pka, your user name is shahar and that is how pka addressed you. If you prefer to be addressed as Shahar that is fine but then you should change your user name to Shahar. Out of curiosity, if you prefer to be addressed as Shahar why did you choose shahar as your user name??

 

[pka]

My name is Shahar with a capital S.

That is really petty of you. This is free help, you get what you pay for.

 

[shahar]

Shahar is morning in Hebrew, I borned in the morning. Shahar is also rising of the sun, sunrise