Proving A x (BUC) = (A x B) U (B x C) in Modern Algebra

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In summary, the conversation is discussing how to prove the statement A x (BUC) = (A x B) U (B x C), where A, B, and C are sets and U represents the union operation. The person asking for help is unsure how to prove it, but the expert provides an example using specific sets and explains that the statement is actually incorrect and should be A x (BUC) = (A x B) U (A x C). The expert also suggests proving the statement by showing that the elements on both sides are the same. Overall, both sides of the equation represent the same concept in different ways.
  • #1
OhyesOhno
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This problem involves modern algebra sets... particularly on cartesian products... so here's the problem:

Prove that A x (BUC) = (A x B) U (B x C)

Note that U here is 'union'

How do I prove that?? I know by the law of De Morgen that A U (BnC) = AUB n AUC but I don't know how to prove that one...
 
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  • #2
Mmmm I'm not so sure that this statement is true.

Suppose C = {1}, B={0}, A={37,38}.

Then Ax(BUC) = Ax{0,1} = {(37,0), (37,1), (38,0), (38,1)}. Meanwhile (AxB)U(BxC) = {(37,0),(38,0)}U{(0,1} = {(37,0),(38,0),(0,1)}

Did you happen to mean Ax(BUC) = (AxB)U(AxC) ?
 
  • #3
Oh yeah, sorry about that. Ax(BUC) = (AxB)U(AxC) is what I meant. Sorry!
 
  • #4
Pick an element (x,y) of the left side and show it's in the right side and conversely. If you describe the contents of the two sides of the equation in words, you'll find you are saying the same thing.
 

1. What is "Modern Algebra" and how is it different from traditional algebra?

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When solving Modern Algebra problems, it is important to first understand the properties and definitions of the algebraic structures involved. It can also be helpful to break down the problem into smaller parts and use different techniques, such as finding patterns or using algebraic identities, to solve it.

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