\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}