i am stumbling again in proving things in maths. the task is to prove that this statement
$A \sim B : \Longleftrightarrow \sum_{a\in A} a = \sum_{b\in B} b $
is an Equivalence Relation on Power Set of {0,1,2} with total order $\leq$.
my start is this:
a) Reflexiv: $A \sim A \Longrightarrow \sum_{a\in A} a = \sum_{a\in A} a$ this is OK
b) Symmetric:.. how do i do this, how can i use the notion of total order here?
i am really stuck, :( i also need to show the equivalence classes here
thanks a lot for help in advance