1. What is Cartesian Product?

The Cartesian product of two sets A and B, denoted by A × B, is the set of all ordered pairs (a, b) where a is in A and b is in B. It's a fundamental concept in set theory and mathematics.

2. How Does the Calculator Work?

The calculator uses the Cartesian product definition:

Where:

• \( A \) — First input set
• \( B \) — Second input set
• \( (a, b) \) — Ordered pair where a is from A and b is from B

Explanation: The calculator takes each element from the first set and pairs it with every element from the second set.

3. Importance of Cartesian Product

Details: Cartesian products are essential in mathematics, computer science, and database theory. They form the basis for relations, joins in databases, and coordinate systems.

4. Using the Calculator

Tips: Enter elements of each set separated by commas. Spaces around commas are ignored. For example: "1, 2, 3" or "a,b,c".

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between Cartesian product and regular multiplication?
A: While both combine elements, Cartesian product creates ordered pairs rather than numerical products.

Q2: Can I calculate Cartesian product of more than two sets?
A: This calculator handles two sets, but the concept extends to any finite number of sets (A × B × C × ...).

Q3: What if my sets contain duplicate elements?
A: The calculator will process them as-is, resulting in duplicate pairs in the output.

Q4: How is Cartesian product used in real life?
A: It's used in database joins, creating test cases in software testing, and defining multidimensional spaces.

Q5: What's the cardinality of a Cartesian product?
A: If set A has m elements and set B has n elements, then A × B has m×n elements.