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This can be read to say "either p q r, or not p", which gives us yet another expression equivalent to the sentences "(p (q))(p (r))" and "(p (q r))".

This can be read to say <math>{}^{\backprime\backprime} \operatorname{either}~ p q r, ~\operatorname{or}~ \operatorname{not}~ p {}^{\prime\prime},</math> which gives us yet another equivalent to the expression <math>\texttt{(} p \texttt{(} q \texttt{))(} p \texttt{(} r \texttt{))}</math> and the expression <math>\texttt{(} p \texttt{(} q r \texttt{))}.</math>  Still another way of writing the same thing would be as follows:

 

Still another way of writing the same thing would be like so:

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In other words, "p is equivalent to p and q and r".

In other words, <math>{}^{\backprime\backprime} p ~\operatorname{is~equivalent~to}~ p ~\operatorname{and}~ q ~\operatorname{and}~ r {}^{\prime\prime}.</math>

Let's pause to refresh ourselves with a few morsels of lemmas bread.  One lemma that I can see just far enough ahead to see our imminent need of is the principle that I canonize as the ''Emptiness Rule''.  It says that a bare lobe expression like "(&hellip; , &hellip;)", with any number of places for arguments but nothing but blanks as filler, is logically tantamount to the proto-typical expression of its type, namely, the constant expression "(&nbsp;)" that <math>\operatorname{Ex}</math> interprets as denoting the logical value ''false''.  To depict the rule in graphical form, we have the continuing sequence of equations:

One lemma that suggests itself at this point is a principle that may be canonized as the ''Emptiness Rule''.  It says that a bare lobe expression like <math>\texttt{( \_, \_, \ldots )},</math> with any number of places for arguments but nothing but blanks as filler, is logically tantamount to the proto-typical expression of its type, namely, the constant expression <math>\texttt{(~)}</math> that <math>\operatorname{Ex}</math> interprets as denoting the logical value <math>\operatorname{false}.</math> To depict the rule in graphical form, we have the continuing sequence of equations:

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