Set Complement And Cartesian Product

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Definition (Set Complement And Cartesian Product)

Let $A$ and $B$ be sets.

• The complement of $B$ in $A$ is the set of elements in $A$ that are not in $B$. We can write this in set builder notation as $$A\setminus B = \{x\mid x\in A \text{ and }x\notin B\}.$$
• The Cartesian product (or cross product, or product) of $A$ and $B$ is the set of ordered pairs $(a,b)$ where $a\in A$ and $b\in B$. We can write the product in set builder notation as $$A\times B = \{(a,b)\mid a\in A\text{ and }b\in B\}.$$