Hi, I wonder if anyone can help me: If $\displaystyle V_1$ is the valuation which assigns F to every propositional variable, and $\displaystyle V_2$ is the valuation which assigns T to every propositional variable, show that every formula $\displaystyle \phi$ such that $\displaystyle \overline {V_1 } \left( \phi \right) = \overline {V_2 } \left( \phi \right) = F$ is logically equivalent to one of the form

$\displaystyle \neg \bigwedge\limits_{i = 1}^n {(C_i \to D_i } )

$

where each $\displaystyle C_i$ is a conjunction of propositional variables and each $\displaystyle D_i$ is a disjunction of propositional variables.

Thanks!