Question

If X, Y and A be three non-empty sets such that A∩X=A∩Y and A∪X=A∪Y , the prove that X=Y? ​

Answer 1

Answer:

When three sets are disjoint sets, their intersection is =ϕ

So, (X ∪ Y ∪ Z) ∩ (X ∩ Y ∩ Z) = (X ∪ Y ∪ Z) ∩ ϕ = ϕ