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Since the expression <math>\texttt{(} p \texttt{(} q \texttt{))(} p \texttt{(} r \texttt{))}</math> involves just three variables, it may be worth the trouble to draw a venn diagram of the situation.  There are in fact a couple of different ways to execute the picture.
 
Since the expression <math>\texttt{(} p \texttt{(} q \texttt{))(} p \texttt{(} r \texttt{))}</math> involves just three variables, it may be worth the trouble to draw a venn diagram of the situation.  There are in fact a couple of different ways to execute the picture.
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Figure&nbsp;1 indicates the points of the universe of discourse ''X'' for which the proposition ''f'' : ''X'' &rarr; '''B''' has the value 1 (= true).  In this ''paint by numbers'' style of picture, one simply paints over the cells of a generic template for the universe ''X'', going according to some previously adopted convention, for instance:  Let the cells that get the value 0 under ''f'' remain untinted, and let the cells that get the value 1 under ''f'' be painted or shaded.  In doing this, it may be good to remind ourselves that the value of the picture as a whole is not in the ''paints'', in other words, the 0, 1 in '''B''', but in the pattern of regions that they indicate.  NB.  In this Ascii version, I use [&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;] for 0 and [&nbsp;`&nbsp;` &nbsp;`&nbsp;] for 1.
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Figure&nbsp;1 indicates the points of the universe of discourse <math>X\!</math> for which the proposition <math>f : X \to \mathbb{B}</math> has the value 1 (<math>= \operatorname{true}</math>).  In this ''paint by numbers'' style of picture, one simply paints over the cells of a generic template for the universe <math>X,\!</math> going according to some previously adopted convention, for instance:  Let the cells that get the value 0 under <math>f\!</math> remain untinted and let the cells that get the value 1 under <math>f\!</math> be painted or shaded.  In doing this, it may be good to remind ourselves that the value of the picture as a whole is not in the ''paints'', in other words, the <math>0, 1\!</math> in <math>\mathbb{B},</math> but in the pattern of regions that they indicate.  (Note.  In this Ascii version, I use [&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;] for 0 and [&nbsp;`&nbsp;` &nbsp;`&nbsp;] for 1.)
    
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{| align="center" cellpadding="10" style="text-align:center; width:90%"
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