symmetric difference

Symmetric difference is one of forms which are infrequently used in elementary level. Given a set $A$ and $B$, it is denoted by $A\vartriangle B$ .

By using preceding terms it means that
$A\vartriangle B=(A-B)\cup (B-A)=(A\cap B^c)\cup (A^c\cap B)$ or
$A\vartriangle B=\left\{ x | (x\in A,  x\notin B)\cup (x\notin A,  x\in B) \right\}$ .

For example, if $A=\left\{ 1,2,3,4 \right\}$  and $B=\left\{ 3,4,5,6 \right\}$ ,
$A\vartriangle B=\left\{ 1,2,5,6 \right\}$ .

Therefore, these below are true.
$A\vartriangle B=B\vartriangle A$   (Commutative law is satisfied)
$(A\vartriangle B)\vartriangle C=A\vartriangle (B\vartriangle C)$   (Associative law is satisfied)
$A\cap (B\vartriangle C)=(A\cap B)\vartriangle (A\cap C)$    (Distributive law in intersection is satisfied)
$A\vartriangle \phi=A$
$A\vartriangle A=\phi$