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What is set theory?

7 years ago

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Answers : (1)

										

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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