Two statements are given below followed by two conclusions numbered (1) and (2). Which of the given conclusions logically follows from the two given statements? Please disregard commonly known facts.
Statements:
Some professors are doctors.
All the doctors are patients.
Conclusions:
Some professors are patients.
No doctor is professor.
Explanation
To solve this problem, we use set theory to represent the groups defined in the statements. Let us define:
P = Professors
D = Doctors
Pt = Patients
Step 1: Analyze the Statements
"Some professors are doctors" implies there is an intersection between the set of professors and the set of doctors:
P∩D=∅
"All the doctors are patients" implies that the set of doctors is a subset of the set of patients:
D⊆Pt
Step 2: Evaluate the Conclusions
Conclusion 1 (Some professors are patients):
Since P∩D=∅, there is at least one element (individual) that is both a professor and a doctor. Since all doctors are patients (D⊆Pt), this individual must also be a patient. Therefore, some professors must be patients.
P∩Pt=∅
Conclusion 1 logically follows.
Conclusion 2 (No doctor is professor):
This statement directly contradicts the first premise, "Some professors are doctors." Therefore, it is false and does not follow.
Conclusion:
Since only Conclusion 1 logically follows from the premises, the correct option is 1: Only (1) conclusion follows.
