Definition:Boolean Satisfiability Problem

Problem
Given a set of binary boolean variables $X$ and a list of one or more logical expresions $L$ find values for all $x \in X$ such that all the expressions in $L$ are true.

Example
If $L$ is defined by:
 * $ \neg x_1 \lor \neg x_2$
 * $x_3$
 * $x_3 \implies x_2$

is then the solution is:
 * $ x_1 = \operatorname{False}$
 * $x_2 = \operatorname{True}$
 * $x_3 = \operatorname{True}$

Also see
The Boolean Satisfiability Problem was the first known NP-Complete problem.