The correct answer is D. Only II and IV and either I or III follow.
The first statement is “Some houses are offices.” This means that there is at least one house that is also an office. The second statement is “Some offices are schools.” This means that there is at least one office that is also a school.
From the first statement, we cannot conclude that all houses are offices, or that all offices are houses. We can only conclude that there is at least one house that is also an office.
From the second statement, we cannot conclude that all offices are schools, or that all schools are offices. We can only conclude that there is at least one office that is also a school.
Therefore, the only conclusions that follow from the two statements are that there is at least one house that is also an office, and there is at least one office that is also a school. This means that conclusions I and IV follow.
Conclusion II, “Some offices are houses,” does not follow from the two statements. This is because the second statement only tells us that there is at least one office that is also a school, not that there is at least one office that is also a house.
Conclusion III, “No house is school,” does not follow from the two statements. This is because the first statement only tells us that there is at least one house that is also an office, not that there is no house that is also a school.
Therefore, the only conclusions that follow from the two statements are that there is at least one house that is also an office, and there is at least one office that is also a school. This means that conclusions I and IV follow, and either conclusion III or conclusion IV follows.