Question

If A and B are two sets such that \(A∪B=A∩B\), then which of the following is correct?

• A. A=ϕ
• B. B=ϕ
• C. A=B
• D. None of these

Answer 1

The Correct Option is C

We are given that \( A \cup B = A \cap B \). Let's analyze this equation.  
- The union of two sets, \( A \cup B \), contains all the elements that are in either \( A \) or \( B \).
- The intersection of two sets, \( A \cap B \), contains only the elements that are in both \( A \) and \( B \).

For the union and intersection of two sets to be equal, every element in \( A \) must also be in \( B \), and vice versa. This implies that \( A \) and \( B \) must be the same set.

Thus, \( A = B \).

So, the correct option is (C): \(A=B\)