1. What is A ∪ B (Union)?

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 a fundamental operation in set theory.

2. How Does the Calculator Work?

The calculator uses the union operation:

Where:

• \( A \) — First set of elements
• \( B \) — Second set of elements
• \( \cup \) — Union operator

Explanation: The calculator combines all unique elements from both sets, removing any duplicates.

3. Importance of Union Calculation

Details: Union operations are essential in mathematics, computer science, database operations, and probability theory. They help combine datasets while maintaining uniqueness.

4. Using the Calculator

Tips: Enter elements for both sets separated by commas. The calculator will combine them and show only unique elements in the result.

5. Frequently Asked Questions (FAQ)

Q1: Does order matter in the input sets?
A: No, the union operation is commutative (A ∪ B = B ∪ A) and order doesn't affect the result.

Q2: What happens with duplicate elements within a set?
A: The calculator treats each set as having unique elements, so internal duplicates within a set are removed.

Q3: How are empty sets handled?
A: The union of any set with an empty set is the original set itself (A ∪ ∅ = A).

Q4: 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.

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