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?

I've been working on this for a few days and i just don't understand, it's due in a few hours. you.the direction of a vector is defined as the angle of the vector in relation to a horizontal line. as a standard, this angle is measured counterclockwise from the positive x-axis. the direction or angle of v in the diagram is α.part a: how can you use trigonometric ratios to calculate the direction α of a general vector v = < x, y> similar to the diagram? part bsuppose that vector v lies in quadrant ii, quadrant iii, or quadrant iv. how can you use trigonometric ratios to calculate the direction (i.e., angle) of the vector in each of these quadrants with respect to the positive x-axis? the angle between the vector and the positive x-axis will be greater than 90 degrees in each case.part cnow try a numerical problem. what is the direction of the vector w = < -1, 6 > ?