# A Question on SAT

A logical formula is unsatisfiable if and only if for the formula to be true, at least one of its variables must be both true and false.

I discovered SAT today, and wanted to try my hands at solving it. I arrived at the above statement as a general principle for any attempt I want to make at solving SAT. Is the principle true?

• Unclear what it states. A logical formula is unsatisfiable if there is no assignment of its variables that turns the fotmula to the logical true. I hope you are aware it is NP complete. – fade2black Jul 26 '17 at 13:24
• @fade2black, I've clarified the question. – Tobi Alafin Jul 26 '17 at 13:34
• Have you tried proving the statement? – adrianN Jul 26 '17 at 13:38
• That condition is not enough. A CNF formula is satisfiable if all of its clauses is true. It is possible that all its variables take false value while the formula may be true. – fade2black Jul 26 '17 at 13:39
• I don't really have any training in formal proofs. So I may have an argument, but I'm not sure if it meets the standards of mathematical rigour others may adopt. – Tobi Alafin Jul 26 '17 at 13:39