Prove or find counterexamples

  • Thread starter mbcsantin
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  • #1
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Main Question or Discussion Point

..using only the definition of the binary product:

for any sets A, B, C in a universe U:

(A x B) x C = A x (B x C)

I have no clue how to even get started with this one. Somebody help me please!!
 

Answers and Replies

  • #2
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Typically you would want to show that both inclusions are true....but in this case.....is the element [tex]((a,b),c) = (a,(b,c))[/tex] ?
 
  • #3
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Typically you would want to show that both inclusions are true....but in this case.....is the element [tex]((a,b),c) = (a,(b,c))[/tex] ?
Yes, they're equal. It's called the Associative Property of Multiplication.

The property which states that for all real numbers a, b, and c, their product is always the same, regardless of their grouping:
(a . b) . c = a . (b . c)
 
  • #4
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I'm sorry..I didn't read the your post correctly if that's the case..was thinking cartesian product.
 
  • #5
HallsofIvy
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Yes, they're equal. It's called the Associative Property of Multiplication.

The property which states that for all real numbers a, b, and c, their product is always the same, regardless of their grouping:
(a . b) . c = a . (b . c)
Then please go back and ask whatever question you are REALLY asking. In your original post, A, B, and C are sets. Now you are telling us that they are real numbers. Also in your first post you asked about proving "A x(B x C)= (A x B)x C" but now you are saying that is the "Associative Property of Multiplication" which apparently you are accepting as true. At this point, I have no idea what your question really is!
 

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