Relation between an unsatisfiable set and a tautology In mathematical logic, satisfiability and validity are elementary concepts of semantics. A formula is satisfiable if it is possible to find an interpretation (model) that makes the formula true. A formula is valid if all interpretations make the formula true. The opposites of these concepts are unsatisfiability and invalidity, that is, a formula is unsatisfiable if none of the interpretations make the formula true, and invalid if some such interpretation makes the formula false.
I read some Midterm exam on logic for computation course. I read this fact on my tutorial note. But I think it's false. 


if set of {$\varphi_1,\varphi_2,...,\varphi_m$} is not satisfiable, then formulate $\neg\varphi_1 \wedge \neg\varphi_2 \wedge ...\wedge  \neg\varphi_m$ is a TAUTOLOGY. 


I think it's False, but in my lecture note is written True. I think it's false. Any hint and tutorial would be highly appreciated.

It is not true. What is true is that $\lnot \varphi_1 \lor \lnot \varphi_2 
\lor \cdots \lor \lnot \varphi_m$ is a tautology.
To see that the sentence with the $\land$ is not necessarily a tautology, let $m=2$, let $\varphi_1=\varphi$ and $\varphi_2=\lnot\varphi$.
