How to prove this just by using Natural Deduction?

Question

I need your help to prove this by using Natural Deduction:
$$(\exists x)(p(x) \implies q) \dashv\vdash (\forall x)(p(x) \implies q).$$ I want to show the proof for both sides. It is a bit easy for me to get the first side from the second side. How can I get the right side from the left side by just using Natural Deduction. Any kind of help will be appreciated.

Answer 1

The right hand side does not follow from the left hand side. If $p(x_1)$ is false, $p(x_2)$ is true, and $q$ is false, then $p(x_1) \implies q$ is true but $p(x_2) \implies q$ is false.