Sets that have the same elements are called **equal sets**. In set theory, two sets \(A\) and \(B\) are said to be equal if and only if they contain exactly the same elements, regardless of the order or repetition of those elements. Formally, sets \(A\) and \(B\) are equal if:

\[
A = B \iff (\forall x \, (x \in A \iff x \in B))
\]

This means that for every element \(x\), \(x\) is an element of set \(A\) if and only if it is also an element of set \(B\).

### Example:

If \( A = \{1, 2, 3\} \) and \( B = \{3, 1, 2\} \), then \( A = B \) because both sets contain the exact same elements, even though they may appear in different order.

Would you like more details or have any questions about set theory?

Here are 5 related questions:
1. What are subsets and how do they differ from equal sets?
2. What is the difference between equal sets and equivalent sets?
3. Can two sets be equal if one contains repeated elements?
4. How are unions and intersections of sets related to equality?
5. What are some real-world applications of equal sets in computer science?

**Tip**: When dealing with sets, always remember that the order and repetition of elements do not matter.

Explore the concept of equal sets in set theory. Learn how two sets are defined as equal if they contain the same elements, regardless of order or repetition. This explanation includes the formula for set equality and examples, suitable for students in Grades 9-12.

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