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Example: Boolean Formula Satisfiability

SAT: Given a Boolean formula in Conjunctive Normal Form (C.N.F.), does there exist a satisfying assignment?

SAT = { B : B is a boolean formula in CNF that is satisfiable by some truth assignment to its variables}

A CNF formula is a boolean formula composed of variables and connectives AND, OR, NOT, IMPLIES, and EQUIV, possibly separated by parentheses.



Let B = \((u_1 \vee \overline{u_2}) \wedge (\overline{u_1} \vee u_2)\).

This is an instance of SAT for which the answer is ``yes''. A satisfying truth assignment is given by t(u1) = t(u2) = T.

On the other hand, the expression \(u_1 \wedge \overline{u_1}\)is an instance of SAT for which the answer is ``no''.


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