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I've tried every which way I can think of to manipulate the algebra using the various laws I was given, but I cannot figure out a way to get $\overline{x+y}$ to convert to only NAND operations using $\overline{x\cdot x}$, $\overline{x\cdot y}$, or $\overline{y\cdot y}$

I've tried using idempotent, DeMorgan's, identity, and double negation laws to no avail.

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en.wikipedia.org/wiki/NAND_logic –  MJD Feb 7 '13 at 3:54

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I’ll use $\mid$ for the connective NAND. You want $\overline{x+y}$; as a first step, this is $(x+y)\mid(x+y)$. Now check that $x+y=(x\mid x)\mid(y\mid y)$, and put the pieces together.

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sigh I've spent a good hour doing various things and I did get to that as a first step, but I can't believe I didn't see that I could easily convert the two $x+y$ to $\overline{\overline{x\cdot x}\cdot\overline{y\cdot y}}$ –  agent154 Feb 7 '13 at 4:07
    
@agent154: Trust me, I know the feeling! –  Brian M. Scott Feb 7 '13 at 4:09

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