Exercise $10\mathrm{.}3\mathrm{.}4$: Give a polynomial$-$time algorithm to solve the problem

$2$SAT, i$.$e$.,$ satisfiability for CNF boolean expressions with only two literals

per clause. Hint: If one of two literals in a clause is false, the other is for ced to

be true. Start with an assumption about the truth of one variable, and chase

down all the consequences for other variables.