1. What Are Set Union and Intersection?

The union of two sets A and B (denoted A ∪ B) is the set of all elements that are in A, or in B, or in both. The intersection (A ∩ B) is the set of all elements that are in both A and B.

2. How Does the Calculator Work?

The calculator uses standard set operations:

Where:

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

Explanation: The calculator processes the input sets, removes duplicates, and performs the mathematical set operations.

3. Importance of Set Operations

Details: Union and intersection are fundamental operations in mathematics, computer science, database operations, and data analysis. They're essential for solving problems in probability, logic, and relational algebra.

4. Using the Calculator

Tips: Enter elements of each set separated by commas. The calculator will automatically remove duplicates and empty values before performing the operations.

5. Frequently Asked Questions (FAQ)

Q1: Does the order of elements matter in the input?
A: No, sets are unordered collections. The calculator will sort the results for display purposes only.

Q2: How are duplicate values handled?
A: Duplicates within a single set are automatically removed before the operations are performed.

Q3: What if my sets have different data types?
A: The calculator treats all values as strings. For mathematical operations, ensure your inputs are numbers.

Q4: What happens if there's no intersection?
A: The intersection result will be empty, which is a valid result (the empty set).

Q5: Can I use this for more than two sets?
A: This calculator handles exactly two sets at a time. For multiple sets, you would need to perform operations sequentially.