Question: This is from Computability and Complexity, Please solve with all the steps Consider an instance of the Satisfiability Problem, specified by clauses Ci, , Ck

This is from Computability and Complexity, Please solve with all the steps

This is from Computability and Complexity, Please solve with all the steps

Consider an instance of the Satisfiability Problem, specified by clauses Ci, , Ck over a set of Boolean variables , , xn-we say that the instanceis monotone if each term in each clause consists of a nonnegated variable; that is, each term is equal to x, for some , rather than Monotone instances of Satisfiability are very easy to solve: They are always sausiable, by settirng each variable equal to I For example, suppose we have the three clauses This is monotone, and indeed the assignment that sets all three variables to 1 satisfies all the clauses. But we can observe that this is not the only satisfying assignment; we could also have set and to 1, and x3 to 0. Indeed, for any monotone instance, it is natural to ask how few variables we need to set to 1 in order to satisfy it. Given a monotone instance of Satisfiability, together with a number k, the problem of Monotone Satisfiability with Few True Variables asks: Is there a satisfying assignment for the instance in which at most k variables are set to 1? Prove this problem is NP-complete

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