Question

UIC 5. (20 pt.) Use the laws of propositional logic to prove that the following compound propositions are tautologies. a. (5 pt.) (p^ q) → (q V r) b. (5 pt) P)Ag)- Vg)A(A-r)- c. (10 pt.) Additional Topics: Satisfiability (10 pt.) A compound proposition is said to be satisfiable if there is an assignment of truth values to its variables that makes it true. For example. p ^ q is true when p = T and q = T;thus, pAqissatsfiable. When no such assignment exists, the compound proposition is said to be unsatisfiable. For example, p ^-p is always false: thus, p ^-p is unsatisfiable. To show that a compound proposition is satisfiable, we need to find at least one assignment of truth values to its variables that makes it true. However, to show that a compound proposition is unsatisfiable, we need to show that every assignment of truth values to its variables makes it false 6. (10 pt., 2.5 pt. each) Determine whether each of the following compound propositions is satisfiable. Justify your answer.

Answer 1

Swite he ro Swicheroo lau

TF F

2-fw) mp 6,pvg) ny, (PVN4) ①n®n@ TF T r

Answer 2

Determine whether each of these compound propositions is satisfiable of unsatisfiable