Show that `A nnB = A uuB` implies `A = B`

Explanation

To show that \( A \cap B = A \cup B \) implies \( A = B \), we will follow these steps:

### Step 1: Assume \( A \cap B = A \cup B \)
We start with the assumption that the intersection of sets \( A \) and \( B \) is equal to the union of sets \( A \) and \( B \).

### Step 2: Show that \( A \subseteq B \)
Let \( x \) be an arbitrary element of set \( A \). By the definition of the union, if \( x \in A \), then \( x \) must also be in \( A \cup B \). Since we have assumed that \( A \cup B = A \cap B \), it follows that \( x \) must also be in \( A \cap B \).

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