If every assignment that models $F$ also models $G$, does it mean that $F=G$?

Question

$G$ 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 $F\neq G$.

It depends on what you mean by $=$, really... – Zhen Lin Dec 25 '12 at 04:09 — Zhen Lin, Dec 25 '12 at 04:09

score 5 · Accepted Answer · answered Dec 25 '12 at 03:21

5

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.

answered Dec 25 '12 at 03:21

JSchlather

15,427

2

Consequently, the answer to the question is "no", and this implies that there exist an infinity of "obscure scenarios" where F≠G. – Doug Spoonwood Dec 25 '12 at 05:44

If every assignment that models $F$ also models $G$, does it mean that $F=G$?

1 Answers1