(Second time posting this problem)This problem is related to Chapter-Sets. Please solve the question using x method. x method means x ∈ A ∩ B

Q. If AUB=Ø, then prove that A=Ø,B=Ø

To prove the statement "If AUB=Ø, then A=Ø and B=Ø", we can use the method of contradiction.

First, assume that either A or B is not equal to Ø. We will consider the cases separately.

Case 1: A is not equal to Ø
If A is not equal to Ø, then there exists an element x that belongs to A. Since x belongs to AUB, it must also belong to AUB. But if x belongs to AUB, then AUB cannot be empty, contradicting our initial assumption. Hence, our assumption that A is not equal to Ø is false.

Case 2: B is not equal to Ø
Similar to Case 1, if B is not equal to Ø, then there exists an element y that belongs to B. Since y belongs to AUB, it must also belong to A. But if y belongs to A, then A cannot be empty, again contradicting our initial assumption. Therefore, our assumption that B is not equal to Ø is false.

Since both assumptions have led to contradictions, it proves that A must be equal to Ø and B must be equal to Ø if AUB is empty.

Hence, we have proved that if AUB=Ø, then A=Ø and B=Ø.