# Math Help - Distributive property for the difference of sets

1. ## Distributive property for the difference of sets

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

2. 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.
$(A\cap B \setminus E)\cap (C\setminus E)$
$=(A\cap B) \cap E^c)\cap (C\cap E^c)$
$=(A \cap B \cap C) \cap E^c$
$=(A \cap B \cap C) \setminus E$