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Is a complement + 1 = 1? For example A' + 1 = 0;

I was thinking it was (I'm new to boolean algebra) since A' = 0, and 0 + 1 in boolean algebra is just 1. Of course, A can be anything, but assuming this is a single variable like B being represented as A, compared to ABCD being represented as A.

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    What do the axioms say is the value of $x+1$ for _any_ $x$?2012-04-04
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    Dilip, x + 1 = 1 for any x. But doesn't the x have to be non-complement? Or can x even be complements?2012-04-04
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    No, that is for **any** $x$ in the algebra.2012-04-04
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    Sorry, Brian not sure I follow. "No" to what?2012-04-04
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    If it makes you feel better, begin your proof with the statement: "Let $x$ denote $A^\prime$. Then, since $x+1=1$ by Axiom $\cdots$, we have that $A^\prime+1=1$."2012-04-04
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    Dilip, if I can specify whether x is complement or non-complement, then why do some laws specify X', such as DeMorgan's Law: X'Y' = X' + Y'?2012-04-04
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    Please re-read Demorgan's Laws **very carefully**. Does one of them _really_ say $X^\prime Y^\prime = X^\prime + Y^\prime$ as you contend, or does it say $(XY)^\prime = X^\prime + Y^\prime$ ??2012-04-04
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    You asked whether $x$ had to a non-complement; I answered ‘No’. (You need to precede a name with '@' in order to ensure that the person sees your comment. I saw yours only because I checked back on a whim.)2012-04-04

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