7.26 Let be a 3cnf-formula. An #-assignment to the variables of is one where each clause contains two literals with unequal truth values. In other words, an #-assignment satisfies without assigning three true literals in any clause.

a. Show that the negation of any #-assignment to o is also an #-assignment.
b. Let #SAT be the collection of 3cnf-formulas that have an #-assignment. Show that we obtain a polynomial time reduction from 3SAT to #SAT by replacing each clause c (y₁ V y2 V ya) with the two clauses (y₁ V 32 V zi) and (Vya V b), where zi is a new variable for each clause c., and b is a single additional new variable.
c. Conclude that #SAT is NP-complete.