3. The Lecture Notes mentions Note that some formulas that look similar to the ones above are not logically equivalent. For example, x (A(x) B(x)) is not logically equivalent to x A(x) x B(x). Verify that x (A(x) B(x)) x A(x) x B(x) by exhibiting a counterexample.

4. Provide an example of a satisfiable first-order logic formula. Show why its satisfiable

5. (Exercise 7.2 from the textbook) Prove that x p(x) x q(x) x (p(x) q(x)) is valid. Suggestion: use proof by contradiction.