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Union and intersection proof 
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#1
Mar708, 11:39 AM

P: 239

1. The problem statement, all variables and given/known data
Prove (A is a union of B)/(A is an intersection of B)=(A/B) is a union of (B/A) 2. Relevant equations 3. The attempt at a solution Could someone first help me translate all of this into plain English. I don't really understand what I need to prove. Would I start off with the contrapositive? Is the contrapositive "If (A/B) is not the union of (B/A), then A is not the union of B/(A is not the intersection of B) and it is not equal to the antecedent"? Could someone please show me where to go from here? Thank you very much 


#2
Mar708, 12:47 PM

P: 213

[tex](A \cup B)/(A \cap B) = (B/A)\cup(A/B)?[/tex] If x is an element of the set on LHS then x is in A or x is in B but x is not in both A and B what can you say about RHS? does it imply something about x that will help you get LHS? 


#3
Mar708, 02:59 PM

P: 363

This is called the symmetric difference of two sets. It can be proven the the associative, distributive, and commutative laws holds with symmetric difference. Those are good exercises.



#4
Mar708, 03:17 PM

P: 239

Union and intersection proof
Thank you very much
Would the contrapositive also prove it? I know how to use the associative property, but I'm sure how how use the others to prove this. I know that, say, A upside B upside C=(A upside B) upside U C=A upside U (B upside U C) I'm not sure how to do that or the others for this problem. Would it be (A U B)/(A upside U B)=A U B/A upside U B? Could some please help me on this? Thank you 


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