Recall the definition of the NP$-$complete problem SATISFIABILITY: given a Boolean propositional logic formula $,$ does $$ have a satisfying truth assignment? We de ne a related problem called DOUBLE$-$SAT: given a Boolean propositional logic formula $,$ does $$ have two different satisfying truth assignments? $($a$)10$ points. Show that DOUBLE$-$SAT is in N P$.($b$)15$ points. Show that DOUBLE$-$SAT is N P$-$complete, by reducing SATISFIABILITY to DOUBLE$-$SAT. That is$,$ show how to use an algorithm that solves DOUBLE$-$SAT to solve SATISFIABILITY.