Question 1026273
We use the fact that X - Y = X ∩ Y', where Y' = set complement of Y.

==> (A-C)-(B-C) = (A∩C')-(B∩C') = (A∩C')∩(B∩C')'

=(A∩C')∩(B'∪C'') =(A∩C')∩(B'∪C) , by using de Morgan's Law and the fact that C'' = C

=(A∩C'∩B')∪(A∩C'∩C) = (A∩C'∩B')∪Ø = A∩C'∩B', by the distributive property, and the fact that C'∩C = Ø.

= A∩B'∩C', by the commutative property.

= (A-B)∩C', by definition of A-B.

= (A-B)-C, by definition of (A-B)-C.