\begin{enumerate} \item using \textit{variable order} $c < a < d < b$:\\ \begin{minipage}{0.5\textwidth} \begin{tabbing} $f$ \= $= (a \lor b \lor c) \land \lnot d$\\ \>$ f_c $ \= $= \lnot d$ \\ \>\>$ f_{ca} $ \= $= \lnot d$ \\ \>\>$ f_{c \lnot a} $ \= $= \lnot d$ \\ \>\>\Rightarrow a does not have an influence\\ \>\>on the formula.\\ \>\>These cofactors can be skipped.\\ \>\>$ f_{cd} $ \= $= \bot$ \\ \>\>$ f_{c \lnot d} $ \= $= \top $ \\ \>$ f_{\lnot c} $ \= $= (a \lor b) \land \lnot d$ \\ \>\>$ f_{\lnot ca} $ \= $= \lnot d = f_{c}$ \\ \>\>$ f_{\lnot c \lnot a} $ \= $= b \land \lnot d$ \\ \>\>\>$ f_{\lnot c \lnot ad} $ \= $= \bot$ \\ \>\>\>$ f_{\lnot c \lnot a \lnot d} $ \= $= b$ \\ \>\>\>\>$ f_{\lnot c \lnot a \lnot db} $ \= $= \top$ \\ \>\>\>\>$ f_{\lnot c \lnot a \lnot db} $ \= $= \bot$ \\ \end{tabbing} \end{minipage} \begin{minipage}{0.5\textwidth} \begin{center} \begin{forest} for tree={circle, draw, no edge, minimum size=2em, inner sep=0pt, s sep=6mm, l sep=6mm} [$f$, rectangle, draw, tikz={\draw [fulldot=.5] () to (c.north);} [,phantom] [$c$, name=c, tikz={\draw [line] () to (d1.north); \draw [dot=.5] () to (a.north);} [$f_{c}$, rectangle, draw, tikz={\draw [fulldot=.5] () to (d1.north west);}] [,phantom] [$a$, name=a, tikz={\draw [line,bend left=30] () to (d1.north); \draw [dot=.5] () to (d2.north);} [$d$, name=d1, tikz={\draw [line] () to (-2,-5); \draw [fulldot=.5] () to (-1,-5);}] [,phantom] [$d$, name=d2, tikz={\draw [line] () to (0.6,-5); \draw [fulldot=.5] () to (b.north);} [,phantom] [$b$, name=b, tikz={\draw [line] () to (1.3,-6.3); \draw [fulldot=.5] () to (2.3,-6.3);}] ] [$f_{\lnot c \lnot a \lnot d}$, rectangle, draw, tikz={\draw [line] () to (b.north east);}] ] [$f_{\lnot c \lnot a}$, rectangle, draw, tikz={\draw [fulldot=.5] () to (d2.north east);}] ] [$f_{\lnot c}$, rectangle, draw, tikz={\draw [fulldot=.5] () to (a.north east);}] ] \end{forest} \end{center} \end{minipage} \item using \textit{variable order} $d < a < b < c$:\\ \begin{minipage}{0.5\textwidth} \begin{tabbing} $f$ \= $= (a \lor b \lor c) \land \lnot d$\\ \>$ f_d $ \= $= \bot$ \\ \>$ f_{\lnot d} $ \= $= a \lor b \lor c$ \\ \>\>$ f_{\lnot da} $ \= $= \top$ \\ \>\>$ f_{\lnot d \lnot a} $ \= $= b \lor c$ \\ \>\>\>$ f_{\lnot d \lnot ab} $ \= $= \top$ \\ \>\>\>$ f_{\lnot d \lnot a \lnot b} $ \= $= c$ \\ \>\>\>\>$ f_{\lnot d \lnot a \lnot bc} $ \= $= \top$ \\ \>\>\>\>$ f_{\lnot d \lnot a \lnot b \lnot c} $ \= $= \bot$ \\ \end{tabbing} \end{minipage} \begin{minipage}{0.5\textwidth} \begin{center} \begin{forest} for tree={circle, draw, no edge, minimum size=2em, inner sep=0pt, s sep=6mm, l sep=6mm} [$f$, rectangle, draw, tikz={\draw [fulldot=.5] () to (d.north);} [,phantom] [$d$, name=d, tikz={\draw [line] () to (-0.5,-2.3); \draw [fulldot=.5] () to (a.north);} [,phantom] [,phantom] [$a$, name=a, tikz={\draw [line] () to (0,-3.6); \draw [dot=.5] () to (b.north);} [,phantom] [,phantom] [$b$, name=b, tikz={\draw [line] () to (0.5,-4.9); \draw [dot=.5] () to (c.north);} [,phantom] [,phantom] [$c$, name=c, tikz={\draw [line] () to (1.3,-6.2); \draw [fulldot=.5] () to (2.3,-6.2);} ] [,phantom] ] [$f_{\lnot d \lnot a \lnot b}$, rectangle, draw, tikz={\draw [line] () to (c.north east);}] ] [$f_{\lnot d \lnot a}$, rectangle, draw, tikz={\draw [line] () to (b.north east);}] ] [$f_{\lnot d}$, rectangle, draw, tikz={\draw [line] () to (a.north east);}] ] \end{forest} \end{center} \end{minipage} \end{enumerate}