Suppose we are given 2 predicates $A(x)$ and $B(x)$ with domain $M$.
Suppose next we are given the following predicate $$\neg (A(x) \land B(x)) \land (\forall x(A(x) \rightarrow B(x)))$$ which we know is true, so $$\neg (A(x) \land B(x)) \land (\forall x(A(x) \rightarrow B(x))) = 1$$
The question is how does it restrict the truth sets of $A(x)$ and $B(x)?$
It is obvious that we have $$\neg (A(x) \land B(x)) = 1 \\ A(x) \land B(x) = 0\\ A(x) = 0 \lor B(x) = 0$$ So from that we get that either truth set for $A(x)$ is $E_A \neq M$ or truth set for $B(x)$ is $E_B \neq M$.
But knowing that $$\forall x(A(x) \rightarrow B(x)) = 1\\ \forall x(\neg A(x) \lor B(x)) = 1$$ I have no idea how to link it to useful information on truth sets of $A(x)$ and $B(x)$, any suggestions?