(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. For any sets A and B. Prove that A∩B⊂A and A∩B⊂B.

To prove that A∩B⊂A, we need to show that every element in the intersection of sets A and B is also present in set A.

To prove this, we can use a direct proof. Let x be an arbitrary element in A∩B. This means x belongs to both set A and set B.

Since x belongs to set A, we can say that x∈A. Therefore, we have shown that every element in A∩B is also present in set A. Hence, A∩B⊂A.

Similarly, to prove that A∩B⊂B, we need to show that every element in the intersection of sets A and B is also present in set B.

Again, let x be an arbitrary element in A∩B. This means x belongs to both set A and set B.

Since x belongs to set B, we can say that x∈B. Therefore, we have shown that every element in A∩B is also present in set B. Hence, A∩B⊂B.

In summary, A∩B⊂A and A∩B⊂B can be proved by using a direct proof and showing that every element in the intersection of sets A and B is also present in set A and set B, respectively.