I am given a statement that says "All teachers wear glasses." And to put it in logical statement, I had a few lines that I thought they sound the same:

Let all humans be in the set of H.

Let all teachers be in the set of T.

Let "is a teacher" be T(x).

Let "does wear glasses" G(x).

$\displaystyle

\forall \; x \epsilon H,\; T(x) \to G(x)

$

$\displaystyle

\forall \; x \epsilon T,\; G(x) \to T(x)

$

$\displaystyle

\forall \;x \epsilon T,\; G (x)\leftrightarrow T(x)

$

$\displaystyle

\forall \;x \epsilon H, x \epsilon T, \; G(x)

$

$\displaystyle

\forall \;x \epsilon T,\; G(x)

$

$\displaystyle

\forall \;x \epsilon H,\: x \epsilon T,\; G(x) \wedge T(x)

$

Out of these statements, which ones are correct? All of these sound logical to me somehow. But I am quite sceptical over the first 2 statements because I remember that p->q is not equals to q->p albeit I have a different set of domain.

thanks...