Login

Articles

Operations on Sets

Print

Union of Sets

Let A and B be two non–empty sets. The union of A and B is the set which consists of all the elements of A and all the elements of B and the common elements of A and B are taken only once.

We denote union of two sets by the symbol ‘U’ and write as A B and usually read as ‘A union B’.
 

Example: Let A = {2, 4, 6, 8, 10} and B = {1, 3, 5, 7, 9} be two sets
So, A B = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

Thus, we can define the union of two sets as:
The union of two sets A and B is the set C which consists of all those elements which are either in A or in B (including those which are in both)

U B = {x: x ε A or x ε B}


Properties of the Operation of Union


1) U B = B A (Commutative law)

2) (U BC = A (B C) (Associative law)

3) A Ф = A (Law of Identity element, Ф is the identity of U)

4) A A = A (Idempotent law)

5) U A = U (Law of U)

Intersection of Sets

Let A and b be two non–empty sets. The intersection of sets A and B is the set of all elements which are common to both A and B.

We denote intersection of two sets by the symbol ‘’ and write as A  B and usually read as ‘A intersection B’.

 

Example: Let A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} and B = {2, 3, 5, 7} be two sets

So, A  B = {2, 3, 5, 7}

 

From the above discussion, the intersection of two sets A and B is the set of all those elements which belong to both A and B.

 B = {x: x ε A and x ε B}


Properties of the Operation of Intersection


1) A ∩ B = B ∩ A (Commutative law)

2) (A ∩ B) ∩ C = A  (B  C) (Associative law)

3) Ф  A = Ф, U ∩ A = A (Law of Ф and U)

4) A ∩ A = A

5) A ∩ (B ∩ C) = (A  B)   (A  C) (Distributive law)
 

Difference of Sets


If A and B are two non–empty sets then the difference of the sets A and B in the same order is the set of elements which belong to A but not to B.
We write it as, A – B and read as A minus B.
Example: Let A = {2, 3, 5, 6, 9} and B = {1, 2, 4, 6, 9}, find A – B and B – A.
A – B = {3, 5}, since the elements 3, 5 belong to A but not to B.
B – A = {1, 4}, since the elements 1, 4 belong to B but not to A.


Now try it yourself! Should you still need any help, click here to schedule live online session with e Tutor!

About eAge Tutoring:


eAgeTutor.com is the premium online tutoring provider. Using materials developed by highly qualified educators and leading content developers, a team of top-notch software experts, and a group of passionate educators, eAgeTutor works to ensure the success and satisfaction of all of its students.
Contact us today to learn more about our guaranteed results and discuss how we can help make the dreams of the student in your life come true!

Reference Links:

    

Archives

Blog Subscription