could anyone show me to do this problem i thinks its false b

could anyone show me to do this problem. i thinks its false, but i can\'t pen a good soltuion?

State whether each item is true or false, and give a brief reason. If the statement is false, your reason should be a counterexample.

For any statements P(x) and Q(x) depending on a variable x, the statement “(x, P(x)) or (x, Q(x)” is equivalent to “x,(P(x) or Q(x))”.

Solution

This statement is false;

because;

statement 1 SAYS

(for all x,P(x)) or (for all x,Q(x))

IS Not equivalent to (for all x, P(x) or P(x));

suppose there are x1,x2,x3.. etc;

FIRST statement says;

P(x1) or P(x1);

P(x1) or P(x2);

P(x1) or P(x3);

:

:

P(x2) or P(x1);

P(x2) or P(x2);

P(x2) or P(x3);

:

:

etc;

But second stament says;

P(x1) or P(x1);

P(x2) or P(x2);

P(x3) or P(x3);

P(x4) or P(x4);