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		,  21:40, 18 August 2009
	
 
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|   | This is not only a logically equivalent DNF but exactly the same DNF expression that we obtained before, so we have established the given equation <math>\texttt{(} p \texttt{(} q \texttt{))(} p \texttt{(} r \texttt{))} = \texttt{(} p \texttt{(} q r \texttt{))}.</math>  Incidentally, one may wish to note that this DNF expression quickly folds into the following form:  |   | This is not only a logically equivalent DNF but exactly the same DNF expression that we obtained before, so we have established the given equation <math>\texttt{(} p \texttt{(} q \texttt{))(} p \texttt{(} r \texttt{))} = \texttt{(} p \texttt{(} q r \texttt{))}.</math>  Incidentally, one may wish to note that this DNF expression quickly folds into the following form:  | 
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| − | {| align="center" cellpadding="8" style="text-align:center; width:90%"  | + | {| align="center" cellpadding="8"  | 
| − | |  | + | | [[Image:Logical Graph (P Q R , (P)).jpg|500px]] || (34)  | 
| − | <pre>
  |   | 
| − | o-----------------------------------------------------------o
  |   | 
| − | |                                                           |
  |   | 
| − | |                     pqr o-------o---o p                   |
  |   | 
| − | |                          \     /                          |
  |   | 
| − | |                           \   /                           |
  |   | 
| − | |                            \ /                            |
  |   | 
| − | |                             @                             |
  |   | 
| − | |                                                           |
  |   | 
| − | |                       (p q r, (p))                        |
  |   | 
| − | |                                                           |  |   | 
| − | o-----------------------------------------------------------o
  |   | 
| − | </pre>
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| − | | (34)  |   | 
|   | |}  |   | |}  | 
|   |  |   |  |