What antigens and antibodies determine blood type?

There are four major blood types determined by presence or absence of two antigens - A and B - on the surface of red blood cells, as well as antibodies A and B found in blood plasma.

Blood type A - red cells have A antigen and B antibody in plasma

Blood type B - red cells have antigen B and antibody A in plasma.

Blood type AB - red cells have both A and B antigens but no antibody in plasma.

Blood type O - red cells have no antigen but there are both antibody A and B in plasma.