1. ## Proving Sets

Hey guys. I posted this yesterday. http://www.mathhelpforum.com/math-he...rs-184242.html. And got infractions, so it was a lesson.

But now that this homework is done. Can you now teach me how to solve this thing? I got squat yesterday, I did not pass anything. So, now I want to know how to solve it. 'Cause the Prof. just let us submit the homework and he dismissed us after. He did not explain/teach us how to do it and what is the right answer.

2. ## Re: Proving Sets

Please tell us what you did.

3. ## Re: Proving Sets

Hello, edriann!

$\displaystyle \text{Prove:}$

$\displaystyle n(A\cup B\cup C)$
. . . . $\displaystyle =\:n(A) + n(B) + n(C) - b(A\cap B) - n(A\cap C) - n(B\cap C ) + n(A\cap B\cap C)$

We know the formula for two sets:
. . $\displaystyle n(P \cup Q) \:=\:n(P) + n(Q) - n(P\cap Q)$

We are given: $\displaystyle A \cup B\cup C$

Group them into two sets: .$\displaystyle A \cup [B \cup C]$

Then we have:

$\displaystyle n(A\cup [B \cup C]) \;=\;n(A) + n(B\cup C) - n(A \cap[B \cup C])$

. . $\displaystyle =\;n(A) + n(B) + n(C) - n(B \cap C) - n([A\cap B]\cup[A\cap C])$

. . $\displaystyle =\;n(A) + n(B) + n(C) - n(B \cap C)$
. . . . $\displaystyle - \bigg[n(A\cap B) + n(A\cap C) - n([A\cap B] \cap[A\cap C]\bigg]$

. . $\displaystyle =\;n(A) + n(B) + n(C) - n(B\cap C) - n(A \cap B) - n(A\cap C) + n(A\cap B\cap C)$