My solution:

Code: Select all

```
ABCDEFGHIJ
JABCDEFGHI
IJABCDEFGH
...
```

The union will never be empty. The meet of subsets could be empty.

My solution:

and so on, where A={1,2,3,4,5}, B={6,7,8,9,10}, ...

My solution:

Code: Select all

```
ABCDEFGHIJ
JABCDEFGHI
IJABCDEFGH
...
```

My solution doesn't violate any of your rules. You should change the second rule to "the meet of any two subsuts on the board has to be empty".