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Math Help - dual statement

  1. #1
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    dual statement

    I need some help with dual statements:

    1) x*y+(xy+1)= dual x+(y*x)+y * 0= or dual x+(y*x)

    2) (x+y)* (0+1) = dual x*y

    Are they correct? thank you!
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  2. #2
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    Re: dual statement

    Quote Originally Posted by tinabaker View Post
    1) x*y+(xy+1)= dual x+(y*x)+y * 0= or dual x+(y*x)
    How is xy different from x*y?

    Could you explain what "dual F" means for some Boolean formula F? Usually, to obtain a dual formula one replaces * with + and vice versa (plus some other replacements). I don't see the dual of x * y from the left-hand side, which is x + y.

    Also, what does = mean here: equality of syntactic expressions or logical equivalence?
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  3. #3
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    Re: dual statement

    xy and x*y are the same.

    the first part of x * y ...then x+(y ...in dual
    "=" just means the same x+(y*x)+y * 0 and or dual x+(y*x)
    just removed y*0 since it just 0...

    but I am not sure about it all...so wanted to check here.
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  4. #4
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    Re: dual statement

    Quote Originally Posted by tinabaker View Post
    the first part of x * y ...then x+(y ...in dual
    Sorry, I did not understand this because the sentence lacks a verb.

    Quote Originally Posted by tinabaker View Post
    "=" just means the same
    Does "same" here mean "are equal character by character" or "have the same truth value for each value of x, y"? Since you say that y*0 is just 0, I think it's the latter...

    Quote Originally Posted by emakarov View Post
    Could you explain what "dual F" means for some Boolean formula F?
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  5. #5
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    Re: dual statement

    Dual means replace 0 by 1, 1 by 0, +by*, *by+

    let me rewrite this thing:
    xy+(xy+1) then dual: x+(yx)
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  6. #6
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    Re: dual statement

    Quote Originally Posted by tinabaker View Post
    xy+(xy+1) then dual: x+(yx)
    I think the dual of xy+(xy+1) is (x+y)*((x+y)*0).
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  7. #7
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    Re: dual statement

    you are correct! I see it now. haha

    so my second: (x+y) (0+1)
    dual is xy+1*0

    Thank you.
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  8. #8
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    Re: dual statement

    Quote Originally Posted by tinabaker View Post
    so my second: (x+y) (0+1)
    dual is xy+1*0
    Correct.
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