2. (8 points) Exercise 7.22 from the textbook. Consider the language DOUBLE-SAT = {(0)| is a SAT instance with at least two satisfying assignments} . Note that this is not 3-SAT. On the other hand, you may use the fact that SAT is NP-complete. (a) (2 points) Show that DOUBLE-SAT E NP. (b) (4 points) Show that DOUBLE-SAT is NP-hard. (c) (2 points) Give an implementation description of the polytime mapping function used in your reduction. 2. (8 points) Exercise 7.22 from the textbook. Consider the language DOUBLE-SAT = {(0)| is a SAT instance with at least two satisfying assignments} . Note that this is not 3-SAT. On the other hand, you may use the fact that SAT is NP-complete. (a) (2 points) Show that DOUBLE-SAT E NP. (b) (4 points) Show that DOUBLE-SAT is NP-hard. (c) (2 points) Give an implementation description of the polytime mapping function used in your reduction