Disjoint sets

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Dec 24th 2009, 07:32 AM
adam_leeds

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
Dec 24th 2009, 07:59 AM
Plato

Quote:

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?

Is your task to show that $A\setminus B,~B\setminus A,~\&~A\cap B$ are pair-wise disjoint?
Dec 24th 2009, 10:06 AM
adam_leeds

Quote:

Originally Posted by Plato

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

This is what im confused about as well it says :
Show that $A\setminus B,~B\setminus A,~\&~A\cap B$ are disjoint sets
Dec 24th 2009, 10:19 AM
Plato

Quote:

Originally Posted by adam_leeds

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

Say that $x\in A\setminus B$ that means that $x\in A,~x\notin B$ .
Thus is it at all possible for $x\in B\setminus A,\text{ or }x\in A\cap B?$
Dec 24th 2009, 10:22 AM
Dinkydoe

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

For example: $x\in A\setminus B \Rightarrow x\notin B \Rightarrow x\notin B\setminus A$ . Thus $A\setminus B$ and $B\setminus A$ are disjoint sets.
Dec 24th 2009, 10:45 AM
adam_leeds

thank you im giving up for now as its xmas tomorrow

merry xmas everyone :)

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