(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 A-B=A then show that A∩B=Ø
To show that A∩B=Ø, we need to prove that there are no elements common between sets A and B if A-B=A.
Let's start by analyzing the given condition: A-B=A.
This condition implies that every element of set A is not present in set B. In other words, set B does not contain any elements that are in set A.
To prove A∩B=Ø, we need to show that there are no elements that both sets A and B have in common.
To start the proof, let's assume that there exists an element x ∈ A∩B, meaning x is both in set A and set B.
Since x is in set A, but not in set B according to the given condition (A-B=A), this assumption leads to a contradiction. Therefore, our initial assumption that an element x ∈ A∩B exists is false.
As a result, we can conclude that there are no elements in common between sets A and B, and thus A∩B=Ø.
So, according to the given condition (A-B=A), we have proven that A∩B=Ø.