1. Provide an example of

i) a first-order logic formula that contains only bound variables (use at least two variables)

ii) a first-order logic formula that contains both, bound variables and free variables (any number > 0 of bound variables and any number > 0 of free variables)

2) Illustrate with one example the De Morgans laws (that is, two examples in total, one for each law), by constructing a specific interpretation in each case.

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.