Question

Let X,Y,Z be three sets such that X U Y=Z, X ∩ Y= Ø.Then prove X=Z-Y

Answer 1

X ∩ Y= Ø
so, x and y have no common elements,
in that case, x and y are disjoint.
and we already know that the union of disjoint - set 2 = set1
for example, a = {1,2,3,4}
                     b = {5,6,7,8}
           then, a U b = {1,2,3,4,5,6,7,8}
            now, {1,2,3,4,5,6,7,8} - {5,6,7,8} (set b)
that is {1,2,3,4} which is nothing but set a.
                                  hence proved