# 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,

• $$\{1,2\} \cap \{2,3\} = \{2\}$$

• $$\{1,2\} \cap \{8,9\} = \{\}$$

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