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Consider the problem in which input is the same as 3-SAT, which is a boolean expression C1∧C2∧···∧Cn where each Ci is an "or" of three literals (each literal can be one of x1 , . . . , xm,¬x1 , . . . ,¬xm). Note that we assume a clause cannot contain duplicate literals (e. g., (x1 ∨ x1 ∨ x2 ) is not allowed). Instead of determining whether there’s a truth assignment on {xi } m i=1 that satisfies this boolean expression (which means it satisfies all the clauses), now we want to determine whether there’s an assignment that satisfies at least n − 1 clauses. Prove that Approx-3SAT is NP-Complete.

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