16 ways 2 objects can be demanded (a logical exercise)

4 ways 2 objects can exist:

1. 01 : B
2. 10: A
3. 11: A and B
4. 00: none

16 ways 2 objects can be demanded:

1. 0001 : neither A nor B
2. 0010 : A and B
3. 0011 : either A and B together or neither of the two
4. 0100 : B by himself
5. 0101 : not A
6. 0110 : B
7. 0111 : not A by himself
8. 1000 : A by himself
9. 1001 : not B
10. 1010 : A
11. 1011 : not B by himself
12. 1100 : exactly one of the two
13. 1101 : at most one of the two
14. 1110 : at least one of the two
15. 1111 : do not care
16. 0000 : null (no comment case)

Key: (only A) or (only B) or (A and B) or (none)
eg: 0101 means B by himself or none => not A