Three Statements followed by three Conclusions are given below. You have to take the Statements to be true even if they seem to be at variance from the commonly known facts. Read all the Conclusions and then decide which of the given Conclusions logically follows/ follow from the Statements, disregarding the commonly known facts: Statement- 1: Some doctors are teachers. Statement- 2: All teachers are engineers. Statement- 3: All engineers are scientists. Conclusion- 1: Some scientists are doctors. Conclusion- 2: All engineers are doctors. Conclusion- 3: Some engineers are doctors. Which one of the following is correct?

Here's a brief explanation:

1. Analyze the Statements:

   • Statement 1: Some doctors are teachers. (D some T)
   • Statement 2: All teachers are engineers. (T all E)
   • Statement 3: All engineers are scientists. (E all S)

2. Derive relationships:

   • From (1) and (2): If some doctors are teachers, and all teachers are engineers, it logically follows that some doctors are engineers. (D some E)
   • From (2) and (3): If all teachers are engineers, and all engineers are scientists, it means all teachers are scientists. (T all S)
   • From (D some E) and (E all S): If some doctors are engineers, and all engineers are scientists, it logically follows that some doctors are scientists. (D some S)

3. Evaluate the Conclusions:

   • Conclusion- 1: Some scientists are doctors.
     • We derived "Some doctors are scientists." This implies that some scientists are doctors. (TRUE)
   • Conclusion- 2: All engineers are doctors.
     • We only know "Some doctors are engineers" (or "Some engineers are doctors"). We cannot conclude that all engineers are doctors. (FALSE)
   • Conclusion- 3: Some engineers are doctors.
     • We derived "Some doctors are engineers." This directly implies that some engineers are doctors. (TRUE)

Therefore, both Conclusion-1 and Conclusion-3 logically follow from the given statements.

The final answer is C) Both Conclusion-1 and Conclusion-3.