When to Use 2-SAT

Use $2$-SAT when: ($1$) You have binary choices for each variable. ($2$) Constraints are "at least one of two conditions must hold." ($3$) You need to find any valid assignment, not count them or find the best one. If you see these patterns, model it as $2$-SAT and use the SCC algorithm.

If constraints involve three or more variables per clause, you need a different approach. $2$-SAT is effective but limited to this specific structure. Do not force problems into $2$-SAT if they do not fit.