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November 30th, 2007, 04:32 AM   #1
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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]
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November 30th, 2007, 05:30 AM   #2
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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.
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November 30th, 2007, 06:55 AM   #3
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∩ = Intersection
∪ = union
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November 30th, 2007, 10:11 AM   #4
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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.
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December 3rd, 2007, 09:47 AM   #5
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I have to prove it using any laws.
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December 3rd, 2007, 12:28 PM   #6
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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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