Human blood comes in four types: O, A, B, or AB, depending upon whether it contains no antigen, A antigen, B antigen, or both A and B antigens. A third antigen, called the Rh antigen, is important in human reproduction. Blood is said to be Rh-positive if it contains this Rh antigen, and Rh-negative otherwise. So for instance, blood is type A+ if it contains the A antigen and the Rh antigen. Blood is type AB- if it contains the A and B antigens but does not contain the Rh antigen.

In a hospital, this data was recorded.

• Twenty-two people were either type A or type AB, 16 of which had the Rh antigen.
  
• Twenty-seven were either type B or type AB, 18 of which had the Rh antigen.
  
• Eight were type AB, two of which were AB-.
• Thirty-five were type O, five of which were O-.

1. How many patients are listed here?

2. How many patients are type B+?

3. How many patients are type A-?

4. How may have exactly two antigens?

The Discrete Mathematics Project