Answer Key for Suggested Exercises 7.5Part I1) 1.N > O 2.N > P / N > (O * P) 3. N ACP 4. O 1,3, MP 5. P 2,3, MP 6. O * P 4,5, Conj 7. N > (O * P) 3-6, CP 2) 1.F > E 2.(F * E) > R / F > R 3. F ACP 4. E 1,3, MP 5. F * E 3,4, Conj 6. R 2,5, MP 7. F > R 3-6 CP 3) 1.G > T 2.(T v S) > K / G > K 3. G ACP 4. T 1,3, MP 5. T v S 4, Add 6. K 2,5, MP 7. G > K 3-6, CP 4) 1.(G v H) > (S * T) 2.(T v U) > (C * D) / G > C 3. G ACP 4. G v H 3, Add 5. S * T 1,4, MP 6. T 5, Com, Simp 7. T v U 6, Add 8. C * D 2,7, MP 9. C 8, Simp 10. G > C 3-9, CP 5) 1.A > ~(A v E) / A > F 2. A ACP 3. ~(A v E) 1,2, MP

4. ~A * ~E 3, DM 5. ~A 4, Simp 6. A v F 2, Add 7. F 5,6, DS 8. A > F 2-7, CP 6) 1.J > (K > L) 2.J > (M > L) 3.~L / J > ~(K v M) 4. J ACP 5. K > L 1,4, MP 6. M > L 2,4, MP 7. ~K 3,5, MT 8. ~M 3,6, MT 9. ~K * ~M 7,8 Conj 10. ~(K v M) 9, DM 11. J > ~(K v M) 4-10, CP 7) 1.M v (N * O) / ~N > M 2. ~M ACP 3. N * O 1,2, DS 4. N 3, Simp 5. ~M > N 2-4, CP 6. ~N > M 5, Trans, DN 8) 1.P > (Q v R) 2.(P > R) > (S * T) 3.Q > R / T 4. P ACP 5. Q v R 1,4, MP 6. R v Q 5, Com 7. ~R > Q 6, DN, Impl 8. ~R > R 3,7, HS 9. R v R 8, Impl, DN 10. R 9, Taut 11. P > R 4-10, CP 12. S * T 2,11, MP 13. T 12, Com, Simp 9) 1.H > (I > N) 2.(H > ~I) > (M v N) 3.~N / M 4. H ACP 5. I > N 1,4, MP 6. ~I 3,5, MT 7. H > ~I 4-6, CP 8. M v N 2,7, MP 9. M 3,8, Com, DS

10) 1.C > (A * D) 2.B > (A * E) / (C v B) > A 3. C v B ACP 4. [C > (A * D)] * [B > (A * E)] 1,2, Conj 5. (A * D) v (A * E) 3,4, CD 6. A * (D v E) 5, Dist 7. A 6, Simp 8. (C v B) > A 3-7, CP 11) 1.M > (K > L) 2.(L v N) > J / M > (K > J) 3. M ACP 4. K ACP 5. K > L 1,3 MP 6. L 4,5, MP 7. L v N 6, Add 8. J 2,7, MP 9. K > J 4-8, CP 10. M > (K > J) 3-9, CP 12) 1.F > (G * H) / (A > F) > (A > H) 2. A > F ACP 3. A ACP 4. F 2,3, MP 5. G * H 1,4, MP 6. H 5, Com, Simp 7. A > H 3-6, CP 8. (A > F) > (A > H) 2-7, CP 13) 1.R > B 2.R > (B > F) 3.B > (F > H) / R > H 4. R ACP 5. B 1,4, MP 6. B > F 2,4, MP 7. F 5,6, MP 8. F > H 3,5, MP 9. H 7,8, MP 10. R > H 4-9, CP 14) 1.(F * G) = H 2.F > G / F = H 3.[(F * G) > H] * [H > (F * G)] 1, Equiv 4. F