I Have to find a Interpretation so that $\Im (\alpha)$ is true. But how can i do that?
$$ \alpha1 = \forall x \exists y \exists z (S(x,b) \to Q(x,y,z) \land \forall v (R(v,y) \to T(v,y))), \omega = \mathbb N $$
for $\alpha1$ as a hint is give: "Each natural number n ≥ 2 has at least one prime factor."
$$ \alpha2 = \forall x \forall y \forall z (S(z) \to ((S(x) \land S(y)) \lor \lnot T(x,y,z))) ,\omega = \mathbb R $$
for $\alpha2$ as a hint is give: "The addition of a rational and an irrational number yields an irrational number."