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Showing posts with the label Theory of Sets

Null set(∅) is a subset of every set - prove it.

 Empty /Null  Set is called the subset of every set,it can be proved  clearly with an example.  • Let,A is a set: A={a,b,c,d}               ∅={} Null set Now, if Null  Set  (∅) is not the sub-set of Set-A; then there must be an element in ∅ which does not belong to set-A But,it is true that there is not a single element in ∅. That is why ∅ is the subset of A-set. Because,a set would not be the subset of an other set in this condition, there must be a different element in that Set . In this way for all sets it can be proved that Null set (∅) is a subset of every set.

Set and It's Elements

 A  set is a group or collection of objects or numbers, considered as an entity  up to itself. Set can be defined  as follows:       •  “A  set is any collection of well-defined and well-distinguished objects. ”       •  “A  set is any collection of objects such that given an object,it is possible to determine whether that object belongs to the given collection or not.” Sets are usually  symbolized by upper case letter,such as A,B,C,X,Y,Z etc. Each object or number in a set is called a member or element of the set. Elements of sets are usually symbolized by lower case letter, such as a,b,c,p,q,r,x,y,z etc.