Correct option is C
Given:
All rugs are mats.
All mats are blankets.
All blankets are quilts.

Conclusion (I): All rugs are quilts.
Conclusion (II): Some quilts are mats.
From the given information, the arrangement will be.
For Conclusion (I): Since the entire circle of "rugs" is inside "mats", "mats" is inside "blankets", and "blankets" is inside "quilts", the circle of "rugs" lies completely inside the circle of "quilts". Therefore, "All rugs are quilts" is true and follows.
For Conclusion (II): Since the "mats" circle is completely contained within the larger "quilts" circle, the overlapping region represents that part of quilts which are definitely mats. Therefore, "Some quilts are mats" is true and follows.
Both conclusions (I) and (II) logically follow.
Final Answer Statement:
Both conclusions (I) and (II) follow.
Conclusion:
Thus, the correct option is (C).