Sets + Mathematical Notation

A dictionary of mathematical notation.

Term	Symbol	Meaning	TEX
Subset	$\subseteq$	If every element of $A$ is in $B,$ we say that $A \subseteq B.$	\subseteq
Proper Subset	$\subset$	If every element of $A$ is in $B,$ but the two sets are guaranteed to not be equal, we say that $A \subset B.$	\subset
Intersection	$\cap$	Used to denote the set of elements that are shared between two sets. $A\ \cap\ B$ denotes the set containing elements shared between $A$ and $B.$	\cap
Union	$\cup$	Used to denote the set that contains all elements of one or many sets, whether they are shared or not. $A\ \cup\ B$denotes the set containing elements contained in $A$ and $B.$	\cup
Complement	$^\complement$	Used to denote items that are in one set but not the other. $A^\complement B$ is the set of elements that are contained in $A$but not in $B.$	\complement
Cross Product	$\times$	Used to denote the set of pairs those first component is in $A$and whose second is in$B.$	\times
In	$\in$	Used to show an item is in a set.	\in
Not In	$\notin$	Used to show an item is not in a set.	\notin
Conjunction	$\wedge$	$P\ \wedge \ Q$ is true if both $P$and$Q$are true.	\land
Disjunction	$\lor$	If either $P$and$Q$are true, then $P\ \lor \ Q$is true.	\lor
Set	$\{\}$	Used to denote a set.	\{\}
Implies	$\implies$	$P \implies Q$ states that $P$ being true means $Q$is true. Doesn't give any info about what happens when $P$is false.	\implies
Iff	$\iff$	If and only if.	\iff
For all	$\forall$	Used to refer to all of the elements within a specific set.	\forall
There exists	$\exists$	Used to declare the existance of one or more of something.	\exists
Negation	$\neg$	$\neg P$ is true when $P$is false.	\neg