Union And Intersection Of Sets

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Definition (Union And Intersection Of Sets)

Let $A$ and $B$ be sets.

• The intersection of $A$ and $B$, written $A\cap B$, is a new set whose elements are those that are in $A$ and in $B$. Using set builder notation, we can write the intersection as $$A\cap B = \{x\mid x\in A \text{ and } x\in B\}.$$
• The union of $A$ and $B$, written $A\cup B$, is a new set whose elements are those that are in $A$ or in $B$ (or both). Using set builder notation, we can write the union as $$A\cup B = \{x\mid x\in A \text{ or } x\in B\}.$$