Union Intersection And Difference Calculator

Set Operations:

\[ A \cup B = \{x \mid x \in A \text{ or } x \in B\} \] \[ A \cap B = \{x \mid x \in A \text{ and } x \in B\} \] \[ A - B = \{x \mid x \in A \text{ and } x \notin B\} \]

Union (A ∪ B):

Intersection (A ∩ B):

Difference (A - B):

Difference (B - A):

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1. What Are Set Operations?

Set operations are fundamental mathematical operations that can be performed on sets, which are collections of distinct elements. The three primary operations are union, intersection, and difference.

2. How Does the Calculator Work?

The calculator performs these operations:

\[ A \cup B = \{x \mid x \in A \text{ or } x \in B\} \] \[ A \cap B = \{x \mid x \in A \text{ and } x \in B\} \] \[ A - B = \{x \mid x \in A \text{ and } x \notin B\} \]

Where:

\( A \cup B \) — Union: all elements in either A or B
\( A \cap B \) — Intersection: elements common to both A and B
\( A - B \) — Difference: elements in A but not in B
\( B - A \) — Difference: elements in B but not in A

3. Importance of Set Operations

Details: Set operations are fundamental in mathematics, computer science, database operations, and many areas of engineering. They form the basis for more complex operations in these fields.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: Are the sets case-sensitive?
A: Yes, "Apple" and "apple" would be considered different elements.

Q2: What happens with duplicate elements in my input?
A: The calculator treats sets as mathematical sets where each element is unique, so duplicates are automatically removed.

Q3: Can I use spaces in my elements?
A: Yes, spaces within elements are preserved (like "New York"), but spaces around commas are trimmed.

Q4: What's the difference between A-B and B-A?
A: A-B gives elements only in A, while B-A gives elements only in B. They're only equal when the sets are identical.

Q5: How are empty sets represented?
A: An empty set is shown as an empty field in the results.