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\}$~$