Definition:Boolean Satisfiability Problem

Problem
Let $X$ be a set of propositional variables.

Let $L$ be a set of one or more propositional formulas constructed using only:
 * elements of $X$
 * the $4$ unary logical connectives $\operatorname{True}$, $\operatorname{False}$, identity, and $\neg$
 * the $16$ binary logical connectives.

The problem is to find truth values for all $x \in X$ such that all the formulas in $L$ are true.

Such a problem is a boolean satisfiability problem.

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

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

Also known as
A boolean satisfiability problem is also known as a SAT problem.

Also see

 * Cook-Levin Theorem, which proves that the Boolean Satisfiability Problem is NP-complete.