Question $2(30$ points$)$: Consider the Double$-$Satisfiability $($DOUBLE$-$SAT$)$ decision problem given

below:

Instance: Boolean formula $f$ in CNF form.

Question: Does $f$ have at least two satisfying truth assignments?

Prove that DOUBLE$-$SAT is NP$-$complete $($Hint reduce SAT to DOUBLE$-$SAT$)$