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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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    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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Answered in the comments: yes, (something) + 1 = 1 in a Boolean algebra. It does not matter if (something) was obtained as a complement of an element, or in another way. Dilip Sarwate made a good suggestion:

If it makes you feel better, begin your proof with the statement: "Let $x$ denote $A'$. Then, since $x+1=1$ by Axiom $\dots$, we have that $A'+1=1$."