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I am searching for the neutral elements of following Boolean expressions:
-NOT
-NAND
-NOR

The neutral element of NOR should be 0 (false) but the others? I think for NOT and NAND there are no neutral elements exisiting.

Thank your for your help!

queenD
  • 3
  • Generally you would consider a neutral element for a binary operation (two inputs). Then $a$ is a neutral element if $ab=ba=b$ for all $b$. NOT is a unary operator, and so would not have a neutral element. – paw88789 Nov 08 '14 at 16:58

1 Answers1

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The operation tables for NOR and NAND look like this:

$$\begin{array}{c||c|c} \mbox{NOR} &0&1 \\\hline 0&1&0\\ \hline 1&0&0 \end{array}$$

$$\begin{array}{c||c|c} \mbox{NAND} &0&1 \\\hline 0&1&1\\ \hline 1&1&0 \end{array}$$

From these tables, we see that neither NOR nor NAND has a neutral element. (The row and column of a neutral element would match the row and column headers of the whole table.)

paw88789
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