Equivalence of Definitions of Symmetric Difference

Theorem
Let $S$ and $T$ be sets.

Then the following definitions of the symmetric difference $S * T$ between $S$ and $T$ are equivalent:

Definition 1

 * $S * T = \left({S \setminus T}\right) \cup \left({T \setminus S}\right)$

Definition 2

 * $S * T = \left({S \cup T}\right) \setminus \left({S \cap T}\right)$

Definition 3

 * $S * T = \left({S \cap \overline T}\right) \cup \left({\overline S \cap T}\right)$

Definition 4

 * $S * T = \left({S \cup T}\right) \cap \left({\overline S \cup \overline T}\right)$