The blood type is determined by the presence of antigens and/or antibodies. If the antigens of a certain blood type are present, then this blood type is present too. But if the antibodies of a blood type are present, then it is impossible to have that blood type because the antibodies will attack the antigens.
In this case, A antigens are present, so all of the blood types with A are possible. B and O blood type has antigens for A blood type, so the blood types that our patient could have are:
A+, A-, AB+ and AB-.