Introduction to subset and proper subset

Introduction to subset and proper subset:

SET:  A set is a collection of distinct objects, considered as an object in its own right.

Example:   A = { 4,9,6,9 } , B = {blue, green , red}

SUBSET:

In mathematics, especially in set theory, a set A is a subset of a set B if A is "contained" inside B. A and B may coincide. The relationship of one set being a subset of another is called inclusion or sometimes containment.

Example : A = { 1,5,3,8,}    , B = { 3,5} ,Here B is subset of A.  That is B `sube`

Proper Subset:

If  A and B are two sets means, A contains all the elements of  B and some additional elements that are not in B.

Example : A = { 3,5,8,10} and B ={ 3,5} .Here B is proper subset of A.

An empty set is always a proper subset of all sets.That is empty set {} is always a proper subset.

This can be denoted as ,  `O/` `subs`

Problems on Subset and Proper Subset :

Problem 1: Find the possible subsets of the set  A = { green ,Yellow,Blue }

Solution:

Given A = { green,yellow,Blue,Black}

We know that empty set is subset of every set.

So subsets of a given set are ,

B = {}

C = {Green,yellow,Blue}

D = { Green,yellow}

E=  { Yellow,Blue}

F = {Green, Blue}

G= {Green}

H = { yellow }

I = {Blue}

The above sets are the subsets of the given set A.

Problem 2 : Find the parent set of the following subsets

B = { 3,8} ,C = { 15,7}, D = { 34,15,8} , E = { 3,7,8}

Solution:

Given B = { 3,8} ,C = { 15,7}, D = { 34,15,8} , E = { 3,7,8}

We know that Subsets are the sets that contains some elements of the Parent set.

So The parent set  might be A = { 3,8,15,7,34,7 }

Problem 3: Express the following sets in-terms of  Venn diagram.

A = { -6 ,8 ,9,0 ,2 } , B = { 0,2,6} , C = { 2,6 } and D = { 34,67,89 }

Solution:

Given A = { -6 ,8 ,9,0 ,2 } , B = { 0,2,- 6} , C = { 2,-6 } and D = { 34,67,89 }

Venn diagram: