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posted by  runningfly2 on 8/3/2008 2:09:30 PM  |  status: Live  

Boolean Algebra

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Discrete Math N/A N/A N/A
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Q: A Boolean algebra can be made into a partially ordered set by letting a b mean a = ab.  Show that a b if and only if b = a + b.  (I couldn't find the correct symbol, so I used instead.  The actual symbol in my book has curved sides, not straight ones and so it looks more like a y on it's side than a V.)

This is my proposed answer.  Any thoughts?
A: If b = a + b then a = ab, by deriving a=a from a=ab.
         a = ab
= a(a + b)
= aa + ab
= a + ab
= a(1 + b)
= a1
=a

Similarly, if a = ab, then b = a + b by deriving b=b from b=a + b.
    b = a + b        
       = ab + b       
       = b(a + 1)           
       = b1              
       = b              

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posted by Angel SK on 8/7/2008 7:22:01 AM  |  status: Live
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Response Details:
suppose ab => a=ab =>a+b =ab+b
                                                 =(a+1)b=1.b=b
conversely ,let  b=a+b => ab = a(a+b)
                                             =aa+ab=a+ab=a(1+b)=a.1=a
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