1. ## Theorem (proof that)

Theorem (proof that)
a) A Δ B = AÚ B if A ∩ B= Φ
b) A ∩ (B Ù C) = (A ∩ B) Ù (A ∩ C)

For a) $A\Delta B=(A\setminus B)\cup(B\setminus A)$ note that if $A\cap B=\emptyset$ then $(A\setminus B)=A$.
For b) Recall $A \wedge (B \vee C) \equiv (A \wedge B) \vee (A \wedge C)$.