# dual statement

• Dec 13th 2011, 10:46 AM
tinabaker
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!
• Dec 13th 2011, 11:57 AM
emakarov
Re: dual statement
Quote:

Originally Posted by tinabaker
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?
• Dec 13th 2011, 12:04 PM
tinabaker
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.
• Dec 13th 2011, 12:16 PM
emakarov
Re: dual statement
Quote:

Originally Posted by tinabaker
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
"=" 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
Could you explain what "dual F" means for some Boolean formula F?

• Dec 13th 2011, 12:19 PM
tinabaker
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)
• Dec 13th 2011, 12:23 PM
emakarov
Re: dual statement
Quote:

Originally Posted by tinabaker
xy+(xy+1) then dual: x+(yx)

I think the dual of xy+(xy+1) is (x+y)*((x+y)*0).
• Dec 13th 2011, 12:28 PM
tinabaker
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.
• Dec 13th 2011, 12:30 PM
emakarov
Re: dual statement
Quote:

Originally Posted by tinabaker
so my second: (x+y) (0+1)
dual is xy+1*0

Correct.