Please explain how you would do this I do not know how to so

Please explain how you would do this I do not know how to solve this. Question is below

Determine whether x(P(x)--> Q(x)) and xP(x)--> xQ(x) are logically equivalent and justify your answer.

Solution

The given two statements are NOT logically equivalent

In order to disprove the above statement, let us assume two statements P and Q and check the truth tables match for each function P and Q

P(x) be a function with number x greater than 100

Q(x) be a function with number x less than 0

x(P(x)--> Q(x)) --> The function is FALSE, since for every x P(x) doesn\'t implies Q(x)

xP(x)--> xQ(x) is also FALSE

Let us assume a number which is 25, then the statement will be TRUE for the second case, since both the statement are false, false-> false will be true

Whereas second statement is False

Hence they are not logically equivalent