
Algebra PreAlgebra and Basic Algebra Math Forum 
 LinkBack  Thread Tools  Display Modes 
November 30th, 2007, 05:32 AM  #1 
Newbie Joined: Nov 2007 Posts: 5 Thanks: 0  sets and relation
Hi I am Vivek. Solve this: A INTERSECTION (A U B)=A Solve this using laws. It is from sets and relation Chapter..[/u][/list] 
November 30th, 2007, 06:30 AM  #2 
Senior Member Joined: Apr 2007 Posts: 2,140 Thanks: 0 
The set theory equation you've gave (A U B) = A is an union, not an intersection (intersection symbol is the upside down U). Since the union of set A and set B is A, set B must be in the area of set A, or they are same.

November 30th, 2007, 07:55 AM  #3 
Senior Member Joined: Sep 2007 From: USA Posts: 349 Thanks: 67 Math Focus: Calculus 
∩ = Intersection ∪ = union 
November 30th, 2007, 11:11 AM  #4 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms 
The question was how to prove A ∩ (A U B) = A What have you covered? What definitions do you use? If you have the de Morgan laws this is easy, of course. 
December 3rd, 2007, 10:47 AM  #5 
Newbie Joined: Nov 2007 Posts: 5 Thanks: 0 
I have to prove it using any laws.

December 3rd, 2007, 01:28 PM  #6 
Senior Member Joined: Oct 2007 From: Chicago Posts: 1,701 Thanks: 3 
A ∪ B = {x(x∈A)⋁(x∈B)} x is a member of A or x is a member of B A ⋂ C = {x(x∈A)⋀(x∈C)} x is a member of both A and C So, A ⋂ (A ⋃ B) = {x[(x∈A)⋁(x∈B)]⋀(x∈A)} I assume you've learned predicate logic, and can reduce the "and" and "or" operators. 

Tags 
relation, sets 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Open Sets and Closed Sets  fienefie  Real Analysis  6  February 24th, 2015 03:14 PM 
relation between ideals and ideals generated by sets...  Lolyta  Abstract Algebra  1  September 30th, 2013 05:35 AM 
Sets relations and function  Equivalence Relation  sachinrajsharma  Algebra  1  March 11th, 2013 12:35 PM 
minor sets sets problem  Jamsisos  Advanced Statistics  1  June 21st, 2012 02:11 PM 
Relation?  jaredbeach  Calculus  0  December 31st, 1969 04:00 PM 