- #1

scorpius1782

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## Homework Statement

The whole problem:

If ##(B \cap C) \subseteq A## then ##[(B \cup C)-A] \subseteq [(B \cup C)-(B \cap C)]##

## Homework Equations

##A-B=A\cap \bar{B}##

##N \subseteq M=\bar{M} \subseteq \bar{N}##

## The Attempt at a Solution

Initially I'm having troubles with ##[(B \cup C)-(B \cap C)]##. I know it should be all the elements that are not shared between B and C but I don't know how to write this out in set notation. I'm hoping that once this is clear I can begin to work the problem backwards so to speak.

For reference the way I've thought of things so far:

I don't really know set problems at all yet so I've begun by thinking of elements inside the sets. So, to start here ##(B \cap C) \subseteq A## means there is an object 'x' in all sets A, B, C.

##[(B \cup C)-A]## Means there is an object 'y' that is in B or C but not in A. And finally: ##[(B \cup C)-(B \cap C)]## 'y' is in a set that is in B or C.

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