Sets, Subsets & Universal Set

Sets:

A Set is made up of a specific group of objects or symbols.

(The objects or symbols are called the Elements of the Set)

Example:

If a set  E  consists of  even numbers,  then

E  =  { 2, 4, 6, 8, … }

Set E  is an Infinite Set.

If  a set  S  is made up of  the  countries of  South America,  then

S  =  { Brazil, Chile, Argentina, …}

Set  S  is a  Finite Set.

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Subsets:

If all the Elements of Set X  are also Elements of  another Set Y, then

X  is  a  Subset  of  Y.

Example:

If   X  =  { sun, moon }    and  Y = { sun, moon, earth }, then

X  C  Y

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Empty set:

If  Set  A  does not have any Elements in it , then it is called an  Empty Set   and is represented by the symbol  Ø

A  =  Ø

(The Empty Set is a Subset of all Sets)

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Universal Set:

The Universal Set contains all Elements  in the problem under consideration.

Complement of a Set:

If  U is the Universal Set  containing Set  A , then

the Complement of Set A is the set of elements  which are  in  U , but not in  A

Example:

If  U = { 11, 13, 15, 17, 19 }  and  A = { 11, 13, 15 }

A’  =  { 17, 19 }

The Complement of the Universal set is the Empty set.

U’ =  Ø

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