For this problem, we imagine Purdue University lasts forever. Inshort order, the singularity occurs, the supernova of the sun isprevented, and it is arranged that Prof. Givan lives forever, teaching ECE 369 each semester. There ensues a countably infiniteseries of semesters of ECE 369, each with a finite set of enrolledstudents. Name the sets of enrolled students in this sequence S_0,S_1, S_2,... While these sets may overlap, we assume each semesterat least one student is taking ECE 369 for the first time. Required:
a. What is the size of the union S of all these sets?
b. What is the smallest size X could be?
c. What is the largest X could be?