Counterexample for the invalidity of the following

Question

Premise 1: $\quad \exists x \ [A(x) \lor B(x)]$

Premise 2:$\quad \exists x \ \lnot A(x)$

Conclusion: $\quad \exists x \ B(x)$

The argument is invalid, but I can't find a counterexample.

Answer 1

Choose $A(0)$ to be true and $A(x)$ to be false for all $x\neq 0$ and $B(x)$ to be false for all $x$.