Intersection

The intersection of two sets $A$ and $B$, denoted $A \cap B$, is the set of elements which are in both $A$ and $B$.

Formally stated, where $C = A \cap B$

$$x \in C \leftrightarrow (x \in A \land x \in B)$$

That is, Iff $x$ is in the intersection $C$, then $x$ is in $A$ and $x$ is in $B$.

For example,

• $\{1,2\} \cap \{2,3\} = \{2\}$
• $\{1,2\} \cap \{8,9\} = \{\}$
• $\{0,2,4,6\} \cap \{3,4,5,6\} = \{4,6\}$