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A cartesian product is the set of all ordered pairs formed by taking one element from each of the two sets defined by 𝐴×𝐵={(𝑥,𝑦)|𝑥𝐴and𝑦𝐵}.

The cardinality of the cartesian product is the product of the cardinalities of the two sets (|𝐴×𝐵|=|𝐴|×|𝐵|)

Example

  • Given 𝐴={𝑎,𝑏,𝑐} and 𝐵={1,2,3}
  • 𝐴×𝐵={(𝑎,1),(𝑎,2),(𝑎,3),(𝑏,1),(𝑏,2),(𝑏,3),(𝑐,1),(𝑐,2),(𝑐,3)}

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