5. Smaller Diagram.

Symbols interpreted.

__________

1. Some y are not-x, or, Some not-x are y.

2. No not-x are not-y, or, No not-y are not-x.

3. No not-y are x.

4. No not-x exist. i.e. No Things are not-x.

5. No y exist. i.e. No houses are two-storied.

6. Some x' exist. i.e. Some houses are not built of brick.

7. No x are y'. Or, no y' are x. i.e. No houses, built of brick, are other than two-storied. Or, no houses, that are not two-storied, are built of brick.

8. All x' are y'. i.e. All houses, that are not built of brick, are not two-storied.

9. Some x are y, and some are y'. i.e. Some fat boys are active, and some are not.

10. All y' are x'. i.e. All lazy boys are thin.

11. All x are y', and all y' are x. i.e. All fat boys are lazy, and all lazy ones are fat.

12. All y are x, and all x' are y. i.e. All active boys are fat, and all thin ones are lazy.

13. No x exist, and no y' exist. i.e. No cats have green eyes, and none have bad tempers.

14. Some x are y', and some x' are y. Or some y are x', and some y' are x. i.e. Some green-eyed cats are bad-tempered, and some, that have not green eyes, are good-tempered. Or, some good-tempered cats have not green eyes, and some bad-tempered ones have green eyes.

15. Some x are y, and no x' are y'. Or, some y are x, and no y' are x'. i.e. Some green-eyed cats are good-tempered, and none, that are not green-eyed, are bad-tempered. Or, some good-tempered cats have green eyes, and none, that are bad-tempered, have not green eyes.

16. All x are y', and all x' are y. Or, all y are x', and all y' are x. i.e. All green-eyed cats are bad-tempered and all, that have not green eyes, are good-tempered. Or, all good-tempered ones have eyes that are not green, and all bad-tempered ones have green eyes.

6. Larger Diagram.

Propositions represented.

__________

             ---------------               ---------------
            |       |       |             |       |       |
            |    ---|---    |             |    ---|---    |
            |   | 0 | 0 |   |             |   |   |   |   |
        1.  |---|---|---|---|         2.  |-1-|---|---|---|
            |   |   |   |   |             |   |   |   |   |
            |    ---|---    |             |    ---|---    |
            |       |       |             |       |       |
             ---------------               ---------------

             ---------------               ---------------
            |       |       |             |       |     0 |
            |    ---|---    |             |    ---|---    |
            |   | 0 | 0 |   |             |   |   |   |   |
        3.  |---|---|---|---|         4.  |---|---|---|---|
            |   |   -   |   |             |   |   |   |   |
            |    ---|---    |             |    ---|---    |
            |       |       |             |       |     0 |
             ---------------               ---------------

             ---------------               ---------------
            | 0     |       |             |       |       |
            |    ---|---    |             |    ---|---    |
            |   | 0 | 0 |   |             |   | 0 | 1 |   |
        5.  |---|---|---|---|         6.  |---|---|---|---|
            |   | 1 |   |   |             |   | 0 |   |   |
            |    ---|---    |             |    ---|---    |
            | 0     |       |             |       |       |
             ---------------               ---------------

             ---------------               ---------------
            |       |       |             |       |     0 |
            |    ---|---    |             |    ---|---    |
            |   | 0 | 0 |   |             |   |   |   |   |
        7.  |---|---|---|---|         8.  |---|---|---|---|
            |   | 0 | 1 |   |             |   | 0 | 0 |   |
            |    ---|---    |             |    ---|---    |
            |       |       |             |       |     0 |
             ---------------               ---------------

                          ---------------
                         |       |       |
                         |    ---|---    |
                         |   | 0 | 0 |   |
  9.  No x are m.  i.e.  |---|---|---|---|
                         |   | 0 |   |   |
                         |    ---|---    |
                         |       |       |
                          ---------------

                             ---------------
                            |       |       |
                            |    ---|---    |
                            |   |   |   |   |
 10.  Some m' are y.  i.e.  |-1-|---|---|---|
                            |   |   |   |   |
                            |    ---|---    |
                            |       |       |
                             ---------------

                             ---------------
                            |       |       |
                            |    ---|---    |
                            |   |   | 0 |   |
 11.  All y' are m'.  i.e.  |---|---|---|-1-|
                            |   |   | 0 |   |
                            |    ---|---    |
                            |       |       |
                             ---------------

The Game of Logic Page 18

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