Cartesian product

A \times B = \{(a, b) : a \in A, b \in B\}

The Cartesian Product of two sets A and B is the set of all Ordered Pairs (a,b) where the first element of order pairs a belongs to first set A and second element of ordered pairs b belongs to second set B.

Example:

A = {1, 3, 6}, B = {x, y}

A x B = \{(1, x), (1, y), (3, x), (3, y), (6, x), (6, y)\}

Cartesian square

A^{2} = A x A = \{(a, b) : a \in A, b \in B\}

The Cartesian squere of set A is the set of all Ordered Pairs (a,b) where both elements of order pairs belongs to first set A.

Example:

A = {1, 3, 6}

A x A = \{(1, 1), (1, 3), (1, 6), (3, 1), (3, 3), (3, 6), (6, 1), (6, 3), (6, 6)\}

Properties of Cartesian Product

|A| = m, |B| = n \Rightarrow |A x B| = m \cdot n

A = \emptyset \lor B = \emptyset \Rightarrow A x B = \emptyset

Keywords: sets, cartesian product, cartesian square

General Information
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Cartesian product
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