# Disjoint sets

• Dec 24th 2009, 07:32 AM
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?

• Dec 24th 2009, 07:59 AM
Plato
Quote:

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
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:

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