I get confused when i think about logical equivalence between conditional statements. For example saying that
If there is variables involved then the statement on the left says that there exists some value of that variable for which P does not imply Q. The statement on the right P and not Q is true for all values of that variable, This is what i understand but i think im wrong because these statements are logically equivalent and are meant to say the same thing about P and Q.
I can understand if they did not include variables but not if they do can someone help explain, thanks.