please use the attached formulas shert to answer

Score: Name: Student Number: /12 Note: For the following three questions, you may use properties 1-21 on our course formula sheet to prove the statements, along with any methods we introduced in class. If you chose to use a property that we have not covered in class or that is not listed on our formula sheet, you must prove the property holds using a truth table. Failure to do so will result in a 2-mark deduction on each question where you use the property. 1. Prove that the following wifs are valid arguments. (a) (x)P() F(x)] m (vw)[F(W) S(x)] (Br)[P(x) A S(:)] (b) (Va)(vy)[(C(x)E(,y)) + A(y)]^(3r)F(x)^(Vr)(F(1) + C(=))(V1) (Ey)E(r,y) [4] (Ex)A(r) () (Wx)(C(x) + (EW(1.1)) (Wx)(V)(W(x,y) S(x, y)) C(m) (Sy)S(m,y) 13. Exportation (exp) (PAq) r) 14. Modus ponens (mp) P P 9 ..9 15. Modus tollens (mt) P9 1 Rules of Inference 1. Commutative Property (com) pVqGVP pA4 2. Associative Property (assoc) (V) Vr => pv (Vr) (phq) Ar = p (qr) 3. Distributive Property (dis) PV (Ar) = (pVg) (Vr) PA (Vr) (PA) (Ar) 4. Identity Property (id) PATP PVFP 5. Complement Property (comp) papF PVT 6. De Morgan's Laws (DM) (A)' apud (PV) pad 7. Definition of Implication (imp) PpVg 8. Double Negation (dn) 16. Conjunction (con) P 9 ..pa 17. Simplification (sim) pa ..9 18. Addition (add) P ..pVg 19. Hypothetical syllogism (hs) P4 4+ 9. Definition of Equivalence (equ) PHp+) (p) 10. Contrapositive (cont) 20. Disjunctive syllogism (ds) PV pl ..9 11. Self reference (self) pephp 12. Self reference (self) PPVP 21. Inconsistency (inc) P