University of California, San Diego: Edward Bender and S. Williamson's "Arithmetic, Logic and Numbers: Logic"
Please read example 9 and example 10 on pages Lo-14 and Lo-15. These readings apply to the topics in 2.2.1.1, 2.2.1.2, and 2.2.2 through 2.2.4. Here is where you will have to apply some of your self-learning skills: you should review what a contrapositive, converse, and inverse are, and use what you have learned about how quantifiers and negation affect one another.
Given a statement in logic, as you have seen with the propositional logic, we can negate it. We can do the same for a statement in predicate logic. Then, once we negate it, how can we rewrite the negated statement as a logically equivalent statement, so that the negation applies to the parts of the statement, rather than the entire statement? Why do we care? Because by doing so, we often simplify the statement or put it into a more convenient form for a particular purpose. In effect, we can study ways to translate from logic to logic in order to obtain a statement that is more convenient for what we might need.