3. Half of Smaller Diagram.

Symbols interpreted.

__________

1. No x are y'.

2. No x exist.

3. Some x exist.

4. All x are y'.

5. Some x are y. i.e. Some good riddles are hard.

6. All x are y. i.e. All good riddles are hard.

7. No x exist. i.e. No riddles are good.

8. No x are y. i.e. No good riddles are hard.

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-|
                            |   |   |
                             -------
                                            -------
                                           | 1 | 0 |
 16.  All y are x, and all x are y.  i.e.  |---|---|
                                           | 0 |   |
                                            -------
                           -------
                          |   |   |
 17.  No x' exist.  i.e.  |---|---|
                          | 0 | 0 |
                           -------
                            -------
                           | 0 | 1 |
 18.  All x are y'.  i.e.  |---|---|
                           |   |   |
                            -------
                          -------
                         | 0 |   |
 19.  No x are y.  i.e.  |---|---|
                         |   |   |
                          -------

                                              -------
                                             |   |   |
 20.  Some x' are y, and some are y'.  i.e.  |---|---|
                                             | 1 | 1 |
                                              -------
                                            -------
                                           | 0 | 1 |
 21.  No y exist, and some x exist.  i.e.  |---|---|
                                           | 0 |   |
                                            -------
                                              -------
                                             |   | 1 |
 22.  All x' are y, and all y' are x.  i.e.  |---|---|
                                             | 1 | 0 |
                                              -------
                                                -------
                                               | 1 |   |
 17.  Some x are y, and some x' are y'.  i.e.  |---|---|
                                               |   | 1 |
                                                -------

The Game of Logic Page 17

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