$G$ and $F$ are formulas, If every assignment that models $G$ also models $F$, does it mean that $F=G$?
The question may be silly, but I'm not sure if there's some obscure scenario where $F\neq G$.
$G$ and $F$ are formulas, If every assignment that models $G$ also models $F$, does it mean that $F=G$?
The question may be silly, but I'm not sure if there's some obscure scenario where $F\neq G$.
You can always extend a formula without changing its truth value by "anding" it with a tautology. So for instance $G=a \wedge b$ and $F=(a \wedge b) \wedge (a \vee \neg a)$ are satisfied by the same models but are not equal.