Exercise $10\mathrm{.}3\mathrm{.}3$: In this exercise, we shall define a family of $3-$CNF expres$-$

sions. The expression $E_n$ has $n$ variables, $x_1,x_2,$dots,$x_n.$ For each set of three

distinct integers between $1$ and $n,$ say $i,j,$ and $k,E_n$ has clauses $(x_i+x_j+x_k)$

and $(\frac{?}{\text{b}\text{a}\text{r}}(x_i)\frac{+}{b}ar(x_j)\frac{+}{b}ar(x_k)).$ Is $E_n$ satisfiable for:

$*!$ a$)n=4?$

$!!$ b$)n=5?$