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\item \lect Compute the propositional formula of the following circuit.
\tikzstyle{branch}=[fill,shape=circle,minimum size=3pt,inner sep=0pt]
\begin{tikzpicture}[label distance=2mm]
\node (a) at (0,0) {$a$};
\node (b) at (0,-1) {$b$};
\node (c) at (0,-2) {$c$};
\node (z) at (8,-1) {$z$};
\node (am) at (1,0) {};
\node (bm) at (1,-1) {};
\node[or gate US, draw, logic gate inputs=nn] at ($(2,-.5)$) (or1) {\tiny OR};
\node[not gate US, draw, logic gate inputs=n] at ($(2,-2)$) (not1) {\tiny NOT};
\node[and gate US, draw, logic gate inputs=nn] at ($(4,-1)$) (and1) {\tiny AND};
\node[not gate US, draw, logic gate inputs=n] at ($(6,-1)$) (not2) {\tiny NOT};
\node (or1m) at (3,-.5) {};
\node (not1m) at (3,-2) {};
\draw (a.east) -| (am.center) |- (or1.input 1);
\draw (b.east) |- (bm.center) |- (or1.input 2);
\draw (or1.output) |- (or1m.center) node[above] {$w$} |- (and1.input 1);
\draw (c.east) |- (not1.input);
\draw (not1.output) |- (not1m.center) node[below] {$x$} |- (and1.input 2);
\draw (and1.output) -- node[below] {$y$} (not2.input);
\draw (not2.output) -- (z);
\end{tikzpicture}