Why this is true?$\exists x \in U, [P(x) \land Q(x)] \Leftrightarrow [(\exists x \in U, P(x)) \land (\exists x \in U, Q(x))]$

Question

$$ [\exists x \in U, P(x) \land Q(x)] \Leftrightarrow [(\exists x \in U, P(x)) \land (\exists x \in U, Q(x))] $$

Answer 1

This is false, its like saying there is someone who is the president of America and there is someone who is president of France, but to say there is someone who is president of both America and France is quite a different thing.