# Math Help - Propositional logic question

1. ## Propositional logic question

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

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

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

Thanks!