Distributive property for the difference of sets

**oldguynewstudent** · November 21st 2009, 04:56 AM

Again thanks for all the help I've been getting on this wonderful site.

I could not find this property in my textbook, yet it has to be used to solve the following step:

[ ( $A_1 \cap A_2 \cap ... \cap A_k$ - B) ] $\cap$ ( $A_k$ $_+$ $_1$ - B)

Is there a distributive property for the difference of sets that is used to write the following?:

[ ( $A_1 \cap A_2 \cap ... \cap A_k$ ) $\cap$ $A_k$ $_+$ $_1$ ] - B

**Plato** · November 21st 2009, 05:19 AM

Originally Posted by oldguynewstudent

[ ( $A_1 \cap A_2 \cap ... \cap A_k$ - B) ] $\cap$ ( $A_k$ $_+$ $_1$ - B)
Is there a distributive property for the difference of sets that is used to write the following?:
[ ( $A_1 \cap A_2 \cap ... \cap A_k$ ) $\cap$ $A_k$ $_+$ $_1$ ] - B

Yes of course.
$(A\cap B \setminus E)\cap (C\setminus E)$
$=(A\cap B) \cap E^c)\cap (C\cap E^c)$
$=(A \cap B \cap C) \cap E^c$
$=(A \cap B \cap C) \setminus E$

Thread: Distributive property for the difference of sets

LinkBack

Thread Tools

Display

Distributive property for the difference of sets

Similar Math Help Forum Discussions

Distributive Property

Why do we want the distributive property?

Please HELP! Distributive property

Distributive Property

Distributive property

Search Tags