Discrete Mathematics by Kenneth Rossen 7th Ed. Chapter 1 Page 89 Example 8

Question

Comments

1st one is  

there exist x which does not follow P or there exist x which follow Q

which is the same as

that there exist x which does not follow P or follow Q (this is nothing but the second statement)

Answer 1

$\exists \text{ symbol favors } \vee$ whereas $\forall \text{ symbol favors } \wedge$

P1: $\exists x (\neg P(x)) \vee \exists x (Q(x))$

P1 will be true if there is no $x$ for which $P(x)$ is true or there is some $x$ for which $Q(x)$ is true.

P2: $\exists x(\neg P(x) \vee Q(x))$

P2: will be true if either Q(x) is true or there is no $x$ for which $P(x)$ is true

So both the statements mean the same and hence are same.