\(A \setminus B = A \setminus (A \cap B)\)

\(A \cup (B \cap C) = (A \cup B) \cap (A \cup C)\)

De Morgan's law
\((A \cap B)^\complement = A^\complement \cup B^\complement\)

De Morgan's law
\((A \cup B)^\complement = A^\complement \cap B^\complement\)

Prove or disprove: If \(A \subseteq B\) and \(A \subseteq C,\) then
$$(B \cap C) - A = (B - A) \cup (C - A)$$