# Thread: Proving a identity in Discrete Math.

1. ## Proving a identity in Discrete Math.

Hello,
some one can help me please and explain to me how to prove this:
$
(A\cap B)\cup(A\cap B\cap \overline{C} \cap D)\cup(\overline{A} \cap B) = B
$

Thank you very much!
I ready don't know to go to it...

2. Originally Posted by Nati
Hello,
some one can help me please and explain to me how to prove this:
$
(A\cap B)\cup(A\cap B\cap \overline{C} \cap D)\cup(\overline{A} \cap B) = B
$
Do you understand that if $P\subseteq Q$ then $P\cup Q=Q~?$

Is it true that $A\cap B\cap \overline{C}\cap D\subseteq A\cap B ~?$

3. Originally Posted by Plato
Do you understand that if $P\subseteq Q$ then $P\cup Q=Q~?$
Yes. i understand that.
Is it true that $A\cap B\cap \overline{C}\cap D\subseteq A\cap B ~?$
but this i can't understand. can you explain it to me please?
thank you.
what $\overline{C}$ mean?

4. Originally Posted by Nati
but this i can't understand. can you explain it to me please? what $\overline{C}$ mean?
You should understand that this is not a homework service nor is it a tutorial service. We help people who already have a basic grasp of the material.
You posted the question. Therefore, you should know what the symbols mean. Frankly, I do not know what $\overline{C}$ means in this context. I guess it probably means the set complement.
That is why you have text material. The identity is still correct.
For every set $X$ it is the case that $X\cap P\subseteq P$. It is true $(A\cap B)\cup (\overline{A}\cap B)=B$.

5. are you fimiler with good artical that explain this subject?
i know what the symbol mean but i thoghut you know its meaning in this context.
Thank you

6. Originally Posted by Nati
are you fimiler with good artical that explain this subject?
You need a textbook, not just an article. I suggest 'Elements Of Set Theory' by Enderton.