Set Theory

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  • Thread starter Chis96
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Main Question or Discussion Point

Can some please explain to me how to solve these two questions?
Let A, B and C be any sets, prove that:
(a) A-B ⊂ A
(b) (A∩B) complement = A complement ∪ B and (A∪B) complement = A complement∩ B complement.
 

Answers and Replies

  • #2
Math_QED
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We usually write out A\B instead of A -B

Anyway, start to write down the definitions and see where you get.

A\B = {x|x ∈ A and x ∉ B}
 
  • #3
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Thank you very much for the correction.
Well.... there are no definitions, it just says let A, B and C be any set, prove that A\B⊂A.
 
  • #4
Math_QED
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Well, look up the definitions! How can you prove something without knowing what the definitions are?
 
  • #5
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No definitions bro, just have to use x to prove it... That's why i'm confused.
 
  • #6
PeroK
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No definitions bro, just have to use x to prove it... That's why i'm confused.
He's talking about the definition of "subset"! As in, what does ##A-B \subset A## actually mean? You can't prove it unless you know what it means.
 
  • #7
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oh... okay basically what it means is that all elements of A\B are contained inside A.
 
  • #8
PeroK
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oh... okay basically what it means is that all elements of A\B are contained inside A.
Yes, although more simply and consistently you could say it means:

Each element of A\B is an element of A.
 
  • #9
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Yes, thank you very much sir.
 

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