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 = .
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 is an instance of SAT for which the answer is ``no''.