1. What is Union of Sets?

The union of two sets A and B is the set of elements which are in A, in B, or in both A and B. It's one of the fundamental operations in set theory.

2. How Does the Calculator Work?

The calculator uses the mathematical definition of set union:

Where:

• \( A \cup B \) — Union of sets A and B
• \( x \in A \) — x is an element of set A
• \( x \in B \) — x is an element of set B

Explanation: The union combines all distinct elements from both sets without duplication.

3. Importance of Set Union

Details: Set union is fundamental in mathematics, computer science, and database operations. It's used in probability, SQL queries, and many algorithms.

4. Using the Calculator

Tips: Enter elements of each set separated by commas. For example: "1, 2, 3" or "apple, banana, orange".

5. Frequently Asked Questions (FAQ)

Q1: Does the order of elements matter in sets?
A: No, sets are unordered collections. {1,2,3} is the same as {3,2,1}.

Q2: What happens with duplicate elements?
A: The calculator automatically removes duplicates as sets contain only unique elements.

Q3: Can I use this for more than two sets?
A: This calculator handles two sets at a time, but you can chain operations for more sets.

Q4: How are empty sets handled?
A: The union of any set with an empty set is the original set itself.

Q5: What's the difference between union and intersection?
A: Union combines all elements from both sets, while intersection includes only elements common to both.