**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*(*u*_{1}) = *t*(*u*_{2}) = *T*.

On the other hand, the expression is an instance of SAT for which the answer is ``no''.