Let be an angle defined on a unit circle, and is the point on this circle defined by , see the picture to the right. Recall also that the angle determining the full circle is 360 (360 degrees). What are the cardinalities (sizes) of the followings 2 sets of points? = { : is defined on = (3 + 5) 1 , for all integer } 10 points Answers in the question below how many times it is relevant angle has to be added in order to arrive at the angle 0 degrees in any multiple of 360 degrees . on the new point will be in set of already created points. In the first questions a new point is created every 5^ B = { : is defined on = 3 5 1 , for all integer } 15 points Provide short justification to all answers (you get only up to 50% of mark without justification).

LIVERPOOL University of Liverpool Department of Computer Science Autumn 2023 Math and Stats for AI and Data Science COMP533 Theory Assignment 1 (study problems) 50/100 Q1, Let 0 be an angle defined on a unit circle, and P is the point on this circle defined by 0, see the picture to the right. Recall also that the angle determining the full circle is 360 (360 degrees). What are the cardinalities (sizes) of the followings 2 sets of points? A= {P : P is defined on 0 = (3i + 5) . 10, for all integer i} 10 points Answers in the question below how many times it is relevant angle has to be added in order to arrive at the angle 0 degrees in any multiple of 360 degrees . on the new point will be in set of already created points. In the first questions a new point is created every 5^ B = {P : P is defined on 0 = =i . 10, for all integer i} 15 points Provide short justification to all answers (you get only up to 50% of mark without justification).Q2, Identify the first 4 (four) values in each of the following sequences, decide whether they have limits whenn - co, and determine the relevant limits if they exist. Sequence A (n) such that A(n) = 2i=1i(it?) , for any integer n > 0. 15 points Hint: elaborate on the fact that 1 1 i(i+1) (i+1) Sequence B(n) such that B(0) = = and B(n) = B(n - 1) +- 1 "(zin+1 , for any integer n > 0. 10 points Hint: use the fact that for any real 0 ;21 x' = X 1-x Provide short justification to your answers (you get only up to 50% of mark without justification). 1