38. No emperors are dentists; All dentists are dreaded by children. No emperors are dreaded by children. Univ. "persons"; m = dentists; x = emperors; y = dreaded by children. xm_{0} + m_{1}y'_{0} ¶ x'y_{1} [Fig. III. Conclusion wrong: right one is "Some persons, dreaded by children, are not emperors." 39. Sugar is sweet; Salt is not sweet. Salt is not sugar. Univ. "things"; m = sweet; x = sugar; y = salt. x_{1}m'_{0} + y_{1}m_{0} ¶ (x_{1}y_{0} + y_{1}x_{0}) [Fig. I (b). Conclusion incomplete: omitted portion is "Sugar is not salt." 40. Every eagle can fly; Some pigs cannot fly. Some pigs are not eagles. Univ. "creatures"; m = creatures that can fly; x = eagles; y = pigs. x_{1}m'_{0} + ym'_{1} ¶ x'y_{1} [Fig. II. Conclusion right. _Solutions for § 8._ SL8 1 2 3 1. cd_{0} + a_{1}d'_{0} + b_{1}c'_{0}; 1 2 3 cd + ad' + bc' ¶ ab_{0} + a_{1} + b_{1} -- = = i.e. ¶ a_{1}b_{0} + b_{1}a_{0} 1 2 3 2. d_{1}b'_{0} + ac'_{0} + bc_{0}; 1 3 2 db' + bc + ac' ¶ da_{0} + d_{1} i.e. ¶ d_{1}a_{0} - =- = 1 2 3 3. ba_{0} + cd'_{0} + d_{1}b'_{0}; 1 3 2 ba + db' + cd' ¶ ac_{0} - -= = 1 2 3 4. bc_{0} + a_{1}b'_{0} + c'd_{0}; 1 2 3 bc + ab' + c'd ¶ ad_{0} + a_{1} i.e. ¶ a_{1}d_{0} -- = = pg156 1 2 3 1 2 3 5. b'_{1}a_{0} + bc_{0} + a'd_{0}; b'a + bc + a'd ¶ cd_{0} - - = = 1 2 3 6. a_{1}b_{0} + b'c_{0} + d_{1}a'_{0}; 1 2 3 ab + b'c + da' ¶ cd_{0} + d_{1} i.e. ¶ d_{1}c_{0} -- = = 1 2 3 1 2 3 7. db'_{0} + b_{1}a'_{0} + cd'_{0}; db' + ba' + cd' ¶ a'c_{0} -- = = 1 2 3 8. b'd_{0} + a'b_{0} + c_{1}d'_{0}; 1 2 3 b'd + a'b + cd' ¶ a'c_{0} + c_{1} i.e. ¶ c_{1}a'_{0} - - = = 1 2 3 9. b'_{1}a'_{0} + ad_{0} + b_{1}c'_{0}; 1 2 3 b'a' + ad + bc' ¶ dc'_{0} - - = = 1 2 3 10. cd_{0} + b_{1}c'_{0} + ad'_{0}; 1 2 3 cd + bc' + ad' ¶ ba_{0} + b_{1} i.e. ¶ b_{1}a_{0} -- = = 1 2 3 11. bc_{0} + d_{1}a'_{0} + c'_{1}a_{0}; 1 3 2 bc + c'a + da' ¶ bd_{0} + d_{1} i.e. ¶ d_{1}b_{0} - = - = 1 2 3 12. cb'_{0} + c'_{1}d_{0} + b_{1}a'_{0}; 1 2 3 cb' + c'd + ba' ¶ da'_{0} -- = = 1 2 3 4 13. d_{1}e'_{0} + c_{1}a'_{0} + bd'_{0} + e_{1}a_{0};