How can we check that this operation is associative ?

[Maths Lover]

hello , there is an example here say that the binary operation which we denote it Δ is associative .
Δ is defiened as follows :
if A,B are two sets then
AΔB=(A-B)U(B-A). and Δ is associative . but the proof is omitted . and I need to know the proof .

 

[micromass]

So, what did you attempt? Where are you stuck?

 

[jedishrfu]

start by subbing in the the union definition and then rearrange terms.

(A ^ B) ^ C ) = ( ( A - B ) U ( B - A ) - C ) U ( C - ( A - B ) U ( B - A ) )

now show some work.