Maximum number of positive literals in 2SAT

Question

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?

Answer 1

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.