Set

Parin Sir > Set
31
May
Complement of  a Set

☼ Complement of  a Set  :   Let  A  be a subset of  the universal set  U, then the complement of  A, denoted by  Aٰ  or  A is defined by :

Aٰ  =  A =  { x : x  U,  x  A }.

Clearly, x  A    x  A.

 e.g.

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31
May
Universal  Set 

☼ Universal  Set  :   In the discussion about sets, all sets are assumed to be the subsets of  a definite set. This definite set is called the universal set. Universal set contains the sets under discussion as subsets. The symbol U i…

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31
May
Super Set

☼ Super Set  :   If  A  B, we say that B is a super set of  A and we write, B  A.

There are infinite supersets of  any finite set but there are finite subsets of  any finite set….

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31
May
Empty Set

☼ Empty Set  :   A set containing no elements at all is called an empty set or a null set or a void set and it is denoted by . In property method,    =  { }.

 e.g. (i) {  x / x

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31
May
Singleton  Set

☼ Singleton  Set  :   A set consisting of  a single element is called a singleton set.

 e.g. { x / x + 5  =  7 }  =  { 2 },  which is a singleton set….

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31
May
How to describe or specify a set ?

Roster Method ( Listing Method ) :   Under this method, we just make a list of  the objects of  the set and put them within braces { }.

 e.g. (i) If  A is set of  first five prime numbers, then A  =  { 2, 3, 5, 7,…

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31
May
Set Theory and Function

Set  :   A well defined collection of  objects is called a set.

The objects in a set are called its elements or members.

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Posted in: Set - Theory,
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