Set Theory & Logic Symbols

Set Theory & Logic

Used in computer science, higher mathematics, and formal logic.

Symbol	Name	Meaning / Usage
$\emptyset$ or $\{\}$	Empty Set	A set containing no elements.
$\in$	Element Of	Belongs to a set ( $a \in A$ ).
$\notin$	Not Element Of	Does not belong to a set ( $a \notin A$ ).
$\cup$	Union	Elements in set A OR set B ( $A \cup B$ ).
$\cap$	Intersection	Elements in set A AND set B ( $A \cap B$ ).
$\subset$	Subset	A is contained inside B ( $A \subset B$ ).
$\forall$	For All	Universal quantifier (true for every instance) ( $\forall x \in \mathbb{R}$ ).
$\exists$	There Exists	Existential quantifier (true for at least one instance) ( $\exists x$ ).
$\Rightarrow$	Implies	If A is true, then B is true ( $A \Rightarrow B$ ).
$\Leftrightarrow$	If and Only If	A and B are logically equivalent ( $A \Leftrightarrow B$ ).
$\therefore$	Therefore	Used to state a conclusion.
$\because$	Because	Used to state a reason.