Question

If A and B are two disjoint sets, then prove that their difference i.e. (A-B) and (B-A) are also disjoint sets.

Answer 1

If A and B are disjoint sets, then they have no element in common.

Say, set A = {1,2,3} and set B = {4,5,6}.
then, we have:
(A-B) to be the set of elements of set A which are not in set B.

1, 2 and 3 are all elements of set A which are not in set B and thus, (A-B) = {1, 2, 3} = A.

Similarly, (B-A) is the set of elements of set B which are not in set A.
Thus, (B-A) = {4, 5, 6} = B.

Therefore, If A and B are disjoint sets, then A-B and B-A are also disjoint sets.