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November 30th, 2007, 04:32 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, 05:30 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, 06:55 AM  #3 
Senior Member Joined: Sep 2007 From: USA Posts: 349 Thanks: 67 Math Focus: Calculus 
∩ = Intersection ∪ = union 
November 30th, 2007, 10:11 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, 09:47 AM  #5 
Newbie Joined: Nov 2007 Posts: 5 Thanks: 0 
I have to prove it using any laws.

December 3rd, 2007, 12:28 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. 

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