The fundamental operations between sets

Between two sets four fundamental operations are defined, each illustrated by the corresponding Venn diagram.

Property — The four operations

• Union: $A\cup B = \{x : x\in A \;\text{oppure}\; x\in B\}$
• Intersection: $A\cap B = \{x : x\in A \;\text{e}\; x\in B\}$
• Complement: $\overline{A} = \{x\in U : x\notin A\}$
• Difference: $A\setminus B = A\cap\overline{B}$

From left to right: union, intersection, complement of $A$ and difference $A\setminus B$.

Links

Topics: Set theory
Concepts: Complement · Venn diagram · Difference of sets · Intersection · Union