3.1. How to compute $f_{5}$ in 5 lines, using only conjunctions and disjunctions (i.e., logical AND and OR)?

#
# Solution.

$$
\begin{aligned}
x_{6} & =x_{1} \vee x_{3} \\
x_{7} & =x_{2} \wedge x_{6} \\
x_{8} & =x_{3} \vee x_{5} \\
x_{9} & =x_{4} \wedge x_{8} \\
x_{10} & =x_{7} \vee x_{9}
\end{aligned}
$$