Maximum number of positive literals in 2SAT MAX 2SAT is NP complete. 

Instead of satisfying the maximum number of clauses, I have a fully satisfiable 2SAT formula and I want to have the maximum number of positive literals in the assignment (such that all the clauses are satisfied, of course). 

What is the difficulty of this problem?
This problem is NP-hard (and in addition hard to approximate and W[1]-hard), because maximum independent set can be reduced to it. Reduction: Each variable represents a vertex and each clause represents an edge.