5. Doctor Armel and Doctor Nike have twenty-four patients. Twelve of the patients have symptom alpha, six of the patients have symptom beta, and fifteen of the patients have symptom gamma. There is only one patient who has all the three symptoms. Two of the patients show symptoms alpha with beta, but do not have symptom gamma. Two of the patients have symptom beta and gamma but do not have symptom alpha. If all of the patients of Doctor Armel and Doctor Nike have at least one of the mentioned symptoms, how many patients are sick with disease Omega, if disease Omega is manifested by symptoms alpha and gamma but not beta? Draw a complete Venn diagram to represent the problem situation.
6. Complete a Venn diagram to represent the following: There are 208 students under the new BS Math course. The Mathematics-Physics-Statistics Department offers math subjects under Prof. Annie, Prof. Ennet and Prof. Yano.
- 4 students take math subjects under all three professors.
- 48 students are enrolled under Prof. Ennet.
- There are twice as many students who are enrolled under both Prof. Ennet and Prof. Yano (but not Prof. Annie) as those who are enrolled under both Prof. Ennet and Prof. Annie (but not Prof. Yano), and 4 times as many as those who are enrolled under all 3 professors.
- 124 students join the math classes of Prof. Yano.
- 27 poor misguided BS Math students do not study any math subject.
- The group of students who are enrolled under both Prof. Ennet and Prof. Yano (but not Prof. Annie) is exactly the same size as the group made up of students who are enrolled under both Prof. Annie and Prof. Yano.
