Does set difference distribute over set intersection?
You are right. As an other proof:
$$A-(B\cap C)=A\cap (B\cap C)^c= A\cap (B^c\cup C^c)=$$
$$(A\cap B^c)\cup (A\cap C^c)=(A-B)\cup(A-C).$$
You are right. As an other proof:
$$A-(B\cap C)=A\cap (B\cap C)^c= A\cap (B^c\cup C^c)=$$
$$(A\cap B^c)\cup (A\cap C^c)=(A-B)\cup(A-C).$$