There are 16 different relations on the set {0, 1}, which can be represented as the power set of the Cartesian product {0, 1} x {0, 1}. These 16 relations are:
1. {} (the empty set)
2. {(0,0)}
3. {(0,1)}
4. {(1,0)}
5. {(1,1)}
6. {(0,0), (0,1)}
7. {(0,0), (1,0)}
8. {(0,0), (1,1)}
9. {(0,1), (1,0)}
10. {(0,1), (1,1)}
11. {(1,0), (1,1)}
12. {(0,0), (0,1), (1,0)}
13. {(0,0), (0,1), (1,1)}
14. {(0,0), (1,0), (1,1)}
15. {(0,1), (1,0), (1,1)}
16. {(0,0), (0,1), (1,0), (1,1)}
Out of these 16 relations, the ones that contain the pair (0, 1) are:
3. {(0,1)}
6. {(0,0), (0,1)}
9. {(0,1), (1,0)}
10. {(0,1), (1,1)}
13. {(0,0), (0,1), (1,1)}
15. {(0,1), (1,0), (1,1)}
16. {(0,0), (0,1), (1,0), (1,1)}
Therefore, there are 7 relations that contain the pair (0, 1).