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` `What is set theory?

7 years ago

Set Theory

Basic Terminology

a)Set:

A set is a collection of well-defined objects. Each individual object is called an element of that set.

For example- the days of the week form a set as

D = { Monday, Tuesday, Wednesday, Thursday, Friday,

Saturday, Sunday }

Tuesday is an element of the set D. We write it as

Tuesday D

However, we are interested in using sets for probabilities.b)

Experiment:

An experiment is defined as any sort of operation whose outcome cannot be predicted in advance with certainty, the sample space S for such an experiment is the set of all possible outcomes that might be observed. For example, rolling a six-sided dice is an experiment.

c)

Event:

An event is defined as a subset of the sample space, which contains any element of a sample space.

d)

Sample Space:

A sample space is the universal set pertinent to a given experiment. The sample space is the set of all possible outcomes of an experiment.

e)

Null Set:

It is a set containing no elements.

f)

Universal Set:

It is the set containing everything in a given context.

g)

Mutually Exclusive Sets or Disjoint Sets:

If there are no elements common to both sets under consideration, they are known as mutually exclusive sets or disjoint sets.

For example, if A = { 1, 2 }, B = { 3, 4 }, then A B =_{}

NOTATIONS FOR A SET:A set can be written in either form:

a)

Roster Notation:To list all the elements of the set one by one.

eg., A = { 1, 2, 3, 4, 5, 6 }b)

Builder Notation:It gives a rule to follow that will tell us how to build the roster.

eg., A = { x 0 < x < 6, x is a whole number }

OPERATIONS:a)

Union of sets:The union of two sets, A and B, written as A U B, is the set that consists of all the elements that belong to A or B or both. For example- A = { 1, 2, 3, 5 } and B = { 1, 2, 4, 6, 7 },

then A U B = { 1, 2, 3, 4, 5, 6, 7 }.b)

Intersection of sets:The intersection of two sets, A and B, written as A

_{}B is the set that consists of all elements that belong to both A and B.

So for the above example, A_{}B = { 1, 2 }.c)

Complement of a set:Complement of a given set is the set containing all the elements in the universal set that are not the members of the given set.

7 years ago

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