Disjoint sets

How can we show that A/B, B/A and A and(Cant do the upside down u symbol) B are disjoint sets?

Thanks for your help in advance

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Originally Posted by adam_leeds

How can we show that A/B, B/A and A and(Cant do the upside down u symbol) B are disjoint sets?

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Is your task to show that $\displaystyle A\setminus B,~B\setminus A,~\&~A\cap B$ are pair-wise disjoint?

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Originally Posted by Plato

Is your task to show that $\displaystyle A\setminus B,~B\setminus A,~\&~A\cap B$ are pair-wise disjoint?

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This is what im confused about as well it says :
Show that $\displaystyle A\setminus B,~B\setminus A,~\&~A\cap B$ are disjoint sets

Quote:

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Originally Posted by adam_leeds

This is what im confused about as well it says :
Show that $\displaystyle A\setminus B,~B\setminus A,~\&~A\cap B$ are disjoint sets

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Say that $\displaystyle x\in A\setminus B$ that means that $\displaystyle x\in A,~x\notin B$.
Thus is it at all possible for $\displaystyle x\in B\setminus A,\text{ or }x\in A\cap B?$

If you want to show that 3 sets A,B,C are pairwise disjoint then you can show the following implications: $\displaystyle x\in A \Rightarrow x\notin B, x\in B\Rightarrow x\notin C, x\in C\Rightarrow x\notin A$

For example: $\displaystyle x\in A\setminus B \Rightarrow x\notin B \Rightarrow x\notin B\setminus A$. Thus $\displaystyle A\setminus B$ and $\displaystyle B\setminus A$ are disjoint sets.

thank you im giving up for now as its xmas tomorrow

merry xmas everyone :)