# Find a truth assignment of 2SAT that has the most number of true variables?

Given a 2SAT instance in CNF where each clause has at most two literals. Let $$m$$ be the number of clauses and $$n$$ be the number of variables et let $$k$$ be a positive number.

Question: Is there a truth assignment such that the number of variables that are true is $$k$$ or more?

I cannot find the name of this problem, if it was already studied? If so, is it NP-hard?

• You are probably interested in a satisfying assignment. – Yuval Filmus Oct 17 at 20:17

Note that the link above is about whether there is a satisfying assignment having at most $$k$$ true variables. This is equivalent to your problem (exercise).