Set theory

Neha BarveLecturer

BioinformaticsSchool Of Biotechnology, DAVV, Indore

• Introduction • Different types of sets

A set is a collection of objects (entities) which are called the members or elements of that set. If we have a set we say that some objects belong (or do not belong) to this set, are (or are not) in the set. We say also that sets consist of their elements.

• Introduction • Different types of sets

Types of set• Null set• Singlet set• Infinite set• Finite set• Disjoint set• Universal set• Subset • Proper set• Improper set• Equal sets• Equivalent set

Null set• There is exactly one set, the empty set, which

has no members at all.• Denoted by "{}," “ ", and “ “ . • It is subset of any set.Singlet set:• A set with only one member is called a

singleton or a singleton set.Disjoint set• Two sets are "disjoint" if they have no objects

in common.

Equivalent set• Two sets are equivalent if they have exactly

the same objects in them. For example,• {a, b, c, d} and {c, a, d, b} are equivalent,

while{a, b, c, d} and {{a, b}, c, d}are not since the former set is a set of four objects, while the latter set is a set with only three objects, one of which itself is a set. It is important to note that two sets which do not have the same number of objects cannot be equivalent.

• Proper subset:• A "proper subset" of a set A is simply a set

which contains some but not all of the objects in A. Proper subsets are denoted using the symbol

• For example, the set {a, b} is a proper subset of the set {a, b, c}:

Improper subset:• An "improper subset" is a subset which can

be equal to the original set; it is notated by the symbol which can be interpreted as "is a proper subset or is equal to".

Subset: • A set A is a subset of a set B if every element

of A is also an element of B. Such a relation between sets is denoted by A B.

Roster method:• A set can be defined by giving all its elements.• Example; A= {1,2,3,4,5,6}Set builder form:• Used for infinite sets.• Sets are defined by some property held by all

members.

Set operations

• set union, • set intersection and • set complement.

Set union

A + B

Set interaction

A B

Complementary set

• A set of all elements not present in A is known as complement of a Ac.

A

Thank you