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 $C=A\cap B$

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

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

For example,

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