Element Proof of (A-B)u(C-B)=(AuC)-B

Question

For all sets A, B, and C, (A-B)∪(C-B)=(A∪C)-B

Answer 1

x is an element of (A-B) u (C-B)

then x is in (A-B) or x is in (C-b)

if x is in A-b then x is in A but not in B.

if x is in C-b then x is in C but not in B.

So x is in A or C but not in B.

Therefore x is in (A u C) - B