9. Some x are y'. i.e. Some lobsters are unselfish. 10. No x are y. i.e. No lobsters are selfish. 11. All x are y'. i.e. All lobsters are unselfish. 12. Some x are y, and some are y'. i.e. Some lobsters are selfish, and some are unselfish. 13. All y' are x'. i.e. All invalids are unhappy. 14. Some y' exist. i.e. Some people are unhealthy. 15. Some y' are x, and some are x'. i.e. Some invalids are happy, and some are unhappy. 16. No y' exist. i.e. Nobody is unhealthy. 4. Smaller Diagram. Propositions represented. __________ ------- ------- | 1 | | | | | 1. |---|---| 2. |---|---| | 0 | | | 1 | | ------- ------- ------- ------- | | | | | 1 | 3. |---|---| 4. |---|---| | | 0 | | | | ------- ------- ------- ------- | | 1 | | | | 5. |---|---| 6. |---|---| | | | | 0 | | ------- ------- ------- ------- | | | | | | 7. |---|---| 8. |---|---| | | 1 | | 0 | 1 | ------- ------- ------- ------- | | | | | | 9. |---|-1-| 10. |---|---| | | | | 0 | 0 | ------- ------- ------- ------- | 1 | | | 1 | 0 | 11. |---|---| 12. |---|---| | 1 | | | | 1 | ------- ------- ------- | | | 13. No x' are y. i.e. |---|---| | 0 | | ------- ------- | | 0 | 14. All y' are x'. i.e. |---|---| | | 1 | ------- ------- | | | 15. Some y' exist. i.e. |---|-1-| | | | -------