Two statements and four conclusions are given. Choose the correct comment…
2019
Two statements and four conclusions are given. Choose the correct comment regarding the conclusions: (Statements): All doctors are honest.
All honest people are fair.
(Conclusions): Some honest people are doctors.
No honest person is a doctor.
Some fair people are doctors.
All fair people are doctors.
- A.
Only conclusions I and III follow
- B.
Only conclusions I and II follow
- C.
Only conclusion II follows
- D.
Only conclusion IV follows
Attempted by 152 students.
Show answer & explanation
Correct answer: A
Given: All doctors are honest. All honest people are fair.
Transitive implication: Every doctor is honest and therefore fair (doctor ⊆ honest ⊆ fair).
From this, if there exists at least one doctor, that doctor is an honest person, so the statement "Some honest people are doctors" follows.
Similarly, any existing doctor is fair, so the statement "Some fair people are doctors" also follows.
The statement "No honest person is a doctor" does not follow; it would contradict the given premises unless there are no doctors at all.
The statement "All fair people are doctors" does not follow because the premises do not imply that every fair person must be a doctor.
Conclusion: Only the statements "Some honest people are doctors" and "Some fair people are doctors" follow (under the usual implicit assumption that at least one doctor exists).