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Among other things, these images make it visually obvious that the constraint on the three boolean variables ''p'', ''q'', ''r'' that we indicate by asserting either of the forms "(p (q))(q (r))" or "''p'' ≤ ''q'' ≤ ''r''" is one that implies a constraint on the two boolean variables ''p'', ''r'' that we indicate by either of the forms "(p (r))" or "''p'' ≤ ''r''", but that it imposes additional constraints on these variables that are not captured by the illative conclusion.

Among other things, these images make it visually obvious that the constraint on the three boolean variables <math>p, q, r\!</math> that is indicated by asserting either of the forms <math>\texttt{(} p \texttt{(} q \texttt{))(} q \texttt{(} r \texttt{))}</math> or <math>p \le q \le r</math> implies a constraint on the two boolean variables <math>p, r\!</math> that is indicated by either of the forms <math>\texttt{(} p \texttt{(} r \texttt{))}</math> or <math>p \le r,</math> but that it imposes additional constraints on these variables that are not captured by the illative conclusion.

One way to view a proposition ''f'' : '''B'''^''k'' &rarr; '''B''' is to consider its ''fiber of truth'', ''f''^&minus;1(1) &sube; '''B'''^''k'', and to regard it as a ''k''-adic relation ''L'' &sube; '''B'''^''k''.

One way to view a proposition ''f'' : '''B'''^''k'' &rarr; '''B''' is to consider its ''fiber of truth'', ''f''^&minus;1(1) &sube; '''B'''^''k'', and to regard it as a ''k''-adic relation ''L'' &sube; '''B'''^''k''.