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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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