There are some special cases I need to know how to prove (and find it very difficult to find everywhere) using the standard logic identities and nothing very specific like axiomatized systems nor special normal forms like Skolem, etc.
First: how can I determine if the following implication is true or false?
( x)[P(x) Q(x)] [ P(x) Q(x)]
A book I have states that it is true, but it doesn't explain why. The exercise pretends the determination of its truth o falsity only using std logical identities like using the implication, the contrapositive, DeMorgan, etc. I also know that only distributes over AND, and only distributes over OR.
Thank you and hope you help me to construct this proof.