Intersection of sets
High school
Consider two sets $A$ and $B$. The intersection of $A$ and $B$, written $A \cap B$, is the set of every element that is in both $A$ and $B$.
Undergraduate
Consider two sets $A$ and $B$. The intersection of sets $A$ and $B$ is
\[A \cap B = \lbrace x : x \in A \text{ and } x \in B \rbrace.\]Examples
Worked examples
- $A = \lbrace 1, 2 \rbrace$ and $B = \lbrace 3, 4 \rbrace$ : $A \cap B = \emptyset$ Elementary
- $A = \lbrace \text{apple}, \text{orange} \rbrace$ and $B = \lbrace \text{orange}, \text{banana} \rbrace$ : $A \cap B = \lbrace \text{orange} \rbrace$ High school
Notes
Sets $A$ and $B$ are disjoint if $A \cap B = \emptyset$.