The $2$SAT$-o+$ decision problem is similar to the $2$ SAT decision problem, except now all clauses

are exclusive$-$OR's, i$.$e$.$ have the form $l_{1}o+l_2$ where $l_1$ and $l_2$ are literals. An instance $C$ of

$2$SAT$-o+$ may be solved with an algorithm that is identical to the Improved $2$SAT algorithm,

except now the graph $G_C$ is undirected. This is because $l_{1}o+l_2$ is logically equivalent to

$(l_1$har$\frac{r}{b}ar(l_2){)}^{{?}^{?}}(\frac{?}{\text{b}\text{a}\text{r}}(l_1)harr{l}_2)$

Thus, both edges are bidirectional $($i$.$e$.$ undirected$)$ and now $G_C$ is referred to as the equivalence

graph. Use the Improved $2$SAT$-o+$ algorithm to solve the following instance of $2$ SAT$-o+.$

$C=\{(x_{1}o+x_6),(x_{1}o+x_2),(x_{3}o+{\stackrel{}{x}}_4),(x_{2}o+{\stackrel{}{x}}_5),(x_{3}o+{\stackrel{}{x}}_6),(x_{4}o+{\stackrel{}{x}}_6)\}$

Draw the equivalence graph and use it to find one or more consistent reachability sets that

yield a satisfying assignment for $C.(20pts)$