Is there an example that proves $( \exists x)(P(x) \land Q(x))$ is not equivalent to $( \exists x)P(x) \land ( \exists x)Q(x)$ Is there an example that proves $(\exists x)(P(x) \land Q(x))$ is not equivalent to $(\exists x)P(x) \land (\exists x)Q(x)$?

Let $P(x)\equiv (x=1)$ and $Q(x)\equiv (x=0)$ and use the fact that  $1\ne 0$
