Relation between sets.





If , in any condition two or more sets appears in discussion they might have some special relation between each other. There are many types or relation that might occur between two or more sets. Those relations are:

Subset:

If one set (A) contains  all the elements that another set (B) contains then the second set (B) is called to be the subset of first set (A) , or set B contains set A.

In symbol we write

A ⊂ B  (A is contained in B) , B ⊃ A (B contains A)

Both symbols above means that set A is a subset of set B.

A set may have two or more subsets.

For example: If set A={1,2,3,4} Then {1} , {2,3} , {4,1} etc. are the subsets of set A.

Note:

*The number of elements a set contains is known as its cardinal number.

*The number of possible subset a set can have is given by the formula 2^s , Where “s” is the cardinal  number  of set A.

*If a set contains all other set that are currently being discussed then the set is called universal set.

Equal set:

Two sets are said to be equal if every element contained by first set is contained by second set and also every elements contained by second set is contained by first set.

equal sets are  sub set of each other.

For example:

If set A={a,b,c,d} and set B={d,a,b,c} Then set A and set B are equal set.

Proper Subset:

If A ⊂ B and A ≠ B(A is not equal to B) then set A is said to be a proper subset of set B. In other words , A set is said to proper subset of another set if every elements contains by the set in contained by another also but the another one also contains some elements not contained in the first set.

For Example:  If A={1,2,3} and B={1,2,3,4} then set A is a proper subset of set B.

Power set:

A set of all subsets of any set is known as power set. It is denoted by “2^s”.

For example:  If S={a,b} then all possible subsets of set S are :  ø , {a} , {b} ,{a,b}

So , 2^s of set S is [ø , {a} , {b} ,{a,b}]

As told on the note above the cardinal number of  power set is given by formula 2^s where “s” is the cardinal number of any set.

Disjoint sets:

Two sets are said to be Disjoint if they dont have any common element.

For example: The set of boys and the set of girls is disjoint , If set A={1,2} and set B={3,4} then set A and B are disjoint.

Intersecting sets:

Two sets are said to be intersecting if some of elements they have are common in both.

For example: If set A={1,2,3} and set B={3,4,5} then set A and set b are  intersecting sets.

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