2.  Half of Smaller Diagram.

Propositions represented.

__________

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

-------            -------
|   |   |          |   |   |
3.  | 1 | 1 |      4.  | 0 | 0 |
|   |   |          |   |   |
-------            -------

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

-------
|   |   |
7.  | 1 | 1 |  It might be thought that the proper
|   |   |
-------     -------
|   |   |
Diagram would be  |   1 1 |, in order to express “some
|   |   |
-------
x exist”:  but this is really contained in “some x are y’.” 
To put a red counter on the division-line would only tell
us “One of the compartments is occupied”, which we
know already, in knowing that one is occupied.
-------
|   |   |
8.   No x are y.  i.e.  | 0 |   |
|   |   |
-------

-------
|   |   |
9.   Some x are y’.  i.e.  |   | 1 |
|   |   |
-------

-------
|   |   |
10.   All x are y.  i.e.  | 1 | 0 |
|   |   |
-------

-------
|   |   |
11.   Some x are y.  i.e.  | 1 |   |
|   |   |
-------

-------
|   |   |
12.   No x are y.  i.e.  | 0 |   |
|   |   |
-------

-------
|   |   |
13.   Some x are y, and some are y’.  i.e.  | 1 | 1 |
|   |   |
-------

-------
|   |   |
14.   All x are y’.  i.e.  | 0 | 1 |
|   |   |
-------
—–­
|   |
15.  No y are x’.  i.e.  |---|
| 0 |
—–­

—–­
| 1 |
16.  All y are x.  i.e.  |---|
| 0 |
—–­

—–­
| 0 |
17.  No y exist.  i.e.  |---|
| 0 |
—–­

—–­
|   |
18.  Some y are x’.  i.e.  |---|
| 1 |
—–­

—–­
|   |
15.  Some y exist.  i.e.  |-1-|
|   |
—–­

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.