théorème des ensembles

**marocker** · November 2nd 2007, 05:43 AM

please help me to do this exercice !

http://i23.servimg.com/u/f23/11/67/15/58/88_bmp10.jpg

thanx

**Soroban** · November 2nd 2007, 07:51 AM

Hello, marocker!

I think I've got the second part . . .

Given: . $\begin{array}{ccc}H_1 & = & A \cap B' \cap C'<br /> \\ H_2 & = & (A \cap B) \cup C \end{array}$

Find: . $[1]\;H_1\cup H_2\qquad [2]\;H_1 \cap H_2$

$[2]\;\;H_1 \cap H_2 \;=\;(A \cap B' \cap C') \cap [(A \cap B) \cup C]$

Distribute: . $A \cap B' \cap C' \cap \overbrace{[(A \cup C) \cap (B \cup C)]}$

Rearrange terms: . $\underbrace{[A \cap (A \cup C)]} \cap\, [\underbrace{(B' \cap C')} \cap (B \cup C)]$

DeMorgan's Law: . . . . $A \quad\;\cap\quad\;\underbrace{[(B \cup C)' \cap (B\cup C)]}$

Then: . . . . . . . . . . . . . $\underbrace{A \qquad\quad\cap\qquad\quad \emptyset}$

Therefore:. . . . . . . . . . . . . . . $\emptyset$

**marocker** · November 2nd 2007, 11:35 AM

and for another question ?

Math Help - théorème des ensembles

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