Union with Set Difference

Theorem

Set Difference Union First Set is First Set

$\paren {S \setminus T} \cup S = S$

Set Difference Union Second Set is Union

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

Set Difference with Union is Set Difference

$\paren {S \cup T} \setminus T = S \setminus T$