Talk:Symmetric Difference is Associative

Can someone add another proof without using the set complement operator? This is because in ZF set theory it cannot be defined, as far as I know. The complement of the empty set is the universe, which should be a proper class and not a set. But ZF only deals with sets.

If it comforts you, think of $R \cup S \cup T$ as the "universe" or the ambient set in this situation. Alternatively, think of $R \cap \overline S$ (the only sense in which complement is used in this proof) as simply an abbreviation for $\{x: x \in R \land x \notin S\}$. I hope that alleviates your concerns. — Lord_Farin (talk) 15:55, 1 July 2015 (UTC)

I already tried that, but I couldn't end up with a complete proof. My math skills are still lacking... Fturco (talk) 17:24, 1 July 2015 (UTC)