Symbol Meaning
| such that, as in {x | x is a rational number}, is a set “x, such that x is a
rational number”
: also used as “such that”
is not an element of
is a subset of (as in AB)
is a proper subset of
is not a proper subset of
A' complement of AHow are some symbolsused in operations on sets?
There are many ways to operate on sets. The following lists some of the more simple
operations on sets, where E, F,and Gare sets:
EFFE
EFFE,in which both are commutative operations;
(EF) GE(FG)
(EF) GE(FG), in which both are associative operations;
(EF) G(EG) (FG)
(EF) G(EG) (FG), in which both are distributive operations.What are the basic set operations?
There are several basic set operations, the most common being the intersection of
sets, union of sets, and the complement of sets. The following lists these operations
(note: the first two operations obey the associative and commutative laws, and togeth-
er they obey the distributive law):
Intersection—The intersection of two sets is the set of elements common to the
two sets. For example, the intersection of sets Aand Bis the set of elements common
to both Aand B. This is usually written as AB. Thus, if A{1, 2, 3, 4} and B{3,
4, 5}, then the intersection of Aand Bwould be {3, 4}.
Union—The union of sets is the combining of members of the sets. For example,
the union of two sets Aand Bis the set obtained by combining members of sets Aand
B. This is usually written as AB. Thus, if A{1, 2, 3, 4} and B{3, 4, 5}, then the
union of Aand Bwould be {1, 2, 3, 4, 5}.
Complement or complementation—When the set of all elements under consider-
ation must be specified, it is called the universal set. And if the universal set is U{1,
2, 3, 4, 5} and A{1, 2, 3}, then the complement of A (or A') is the set of all elements
in the universal set that are not A,or {4, 5}. The intersection between a set and its 125