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- I: Some scientists are doctors. Conclusion- II: All engineers are doctors. Conclusion- III: Some engineers are doctors. Which one of the following is correct?

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). Let's evaluate each conclusion: Conclusion I: Some scientists are doctors. From Statement 1 (Some doctors are teachers) and Statement 2 (All teachers are engineers), it follows that some doctors are engineers (D some E). From this (Some doctors are engineers) and Statement 3 (All engineers are scientists), it follows that some doctors are scientists (D some S). Therefore, Some scientists are doctors. Conclusion I is logically TRUE. Conclusion II: All engineers are doctors. From Statement 1 (Some doctors are teachers) and Statement 2 (All teachers are engineers), we know that some doctors are engineers. This means there's an overlap, but it does not imply that the entire set of engineers consists of doctors. There could be engineers who are not teachers and therefore not doctors. Conclusion II is logically FALSE. Conclusion III: Some engineers are doctors. From Statement 1 (Some doctors are teachers) and Statement 2 (All teachers are engineers), if some doctors are part of the teacher group, and the entire teacher group is part of the engineer group, then those 'some doctors' must also be engineers. Therefore, some doctors are engineers, which means some engineers are doctors. Conclusion III is logically TRUE. Since both Conclusion I and Conclusion III are logically true, Option C is the correct answer.