# Design an algorithm,have polynomial complexity for deciding satisfiability of a 1-conjective Normal Form boolean formula

I undetstand each part of the word group in this question. I have search for a while but I still can't understand what the whole question want me to do. I will state what I know and give an assumption of what I should do, I would be appreciate if someone can guide me.

First a boolean formula is satisfiable if it can be made TRUE by assigning appropriate logical values, so "deciding the satisfiability" means to decide whether this boolean formula can be made a TRUE result.

Then for conjunctive normal form is means a conjunctive of clauses which are disjunctive inside. and 1-conjunctive normal form means each clause contains one variable, such like A\wedge B.

Now is the problem, what means an algorithm to decide it? I mean isn't the way to decide the satifiability of a boolean formula is try ture and false assiagnments to find whether it can be TRUE as a result? For example: since it is conjunctive normal form so each result of clauses needs to be TRUE, and it is 1-conjunctive normal form, so each variables need to be TRUE. Is this one an accpaptable algorithm to deal with the question?

When the entire logic formula is just a single conjunction of variables, the only way it is not satisfiable is if it contains both $a$ and $\neg a$. If there is no variable which is contained both positive and negatively in the formula, the formula is satisfiable.