Set Theory (Not too difficult)

  • Thread starter gutnedawg
  • Start date
  • #1
gutnedawg
35
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Homework Statement


describe exactly when
x intersecting (y union z) = (x intersecting y) union z

Homework Equations





The Attempt at a Solution



I just for some reason cannot see this solution and need a shove in the right direction
 

Answers and Replies

  • #2
murmillo
118
0
Try drying a Venn diagram. It turns out that the shaded areas are not the same. Then ask yourself what you must do to one or more of the sets so that the shaded areas will be the same.
 
  • #3
lanedance
Homework Helper
3,304
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or you could use relation
[tex] x \cap (y \cup z ) = (x \cap y) \cup ( x \cap z) [/tex]

this shoudln't be too difficult to prove if need be
 
  • #4
murmillo
118
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Ah, I didn't know that relation. I don't know if the original poster is supposed to know that relation. If that identity can be assumed, then the problem is much easier.
 
  • #5
gutnedawg
35
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so lanedance I can just say that if

[tex]x\cap z = z [/tex]

then the first equality holds?
 
  • #6
lanedance
Homework Helper
3,304
2
yeah, so
[tex] x\cap z = z \rightarrow[/tex]
[tex] x \cap (y \cup z ) = (x \cap y) \cup z [/tex]

you should convince yourself through venn diagrams or proof, why this is case
 
Last edited:

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