Here's a question:

For part (a) is it sufficient to show using the commutative law of union and the commutative law of intersection that:

$\displaystyle (A \star B) = (A \cup B) \backslash (A \cap B)$

$\displaystyle = (B \cup A) \backslash (B \cap A) = (B \star A)$

Or do I need to show some other steps?

Also, could anyone please show me how to prove that:

$\displaystyle (A \star B) \star C = (A \cap B \cap C) \cup (C \backslash (A \cup B)) \cup (A \backslash (B \cup C)) \cup (B \backslash (A \cap C))$

P.S.: is that a simplification of:

$\displaystyle (A \star B) \star C = (((A \cup B) \backslash (A \cap B)) \cup C) \backslash (((A \cup B) \backslash (A \cap B)) \cap C)$ ?