2-satisfiability.Given a boolean formula in conjunctive normal form with Mclauses and Nvariables such that each clause has exactly two literals (where a literal is either a variable or its negation), find a satisfying assignment (if one exists). Hint: Form the implication digraphwith 2Nvertices (one per literal). For each clause x + y,include edges from y'to x and from x'to y. Claim:The formula is satisfiable if and only if no literal x is in the same strong component as its negation x'. Moreover, a topological sort of the kernel DAG(contract each strong component to a single vertex) yields a satisfying assignment.
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