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# Intersection of two sets

The intersection of two sets $A$ and $B$ consists of the elements that are in both $A$ and $B$. The set is written $A\cap B$.

$$\{1,\Tred{2},3\}\cap \{0,\Tred{2},4\} = \{\Tred{2}\}$$

The intersection of the odd and even numbers is empty.

The intersection of the multiples of $2$ and of the multiples of $3$ is the set of the multiples of $6$.

The intersection $A\cap B$ is a subset of both $A$ and $B$.

Two sets are mutually exclusive, or disjoint, if they have no elements in common. Their intersection is empty.

The set of the people who lived in the 15th century and the set of the people who live today are mutually exclusive.

Intersection of two sets