5. Use a floor or a ceiling function to find cardinalities of following sets: a) [{x € Z*]x is multiple of 5 and x 5 622}| = b) [{x € z* \x is multiple of 5 and 235 s x S 622}| = %3D

Construct a proof of the Bolzano-Weierstrass Theorem using the Nested Interval Theorem

1.47. Which of the following sets are equal? A = {x:x² - 4x + 3 = 0}, B = {x:x²-3x + 2 = 0}, C = (x:xEN, x <3}, D= (x:xEN, x is odd, x < 5}, E = {1,2}, F = {1,2, 1}, G=(3, 1), H = {1, 1,3} 1.48. List the elements of the following sets if the universal set is the English alphabet U = {a, b, c,..., y, z}. Furthermore, identify which of the sets are equal. A = {x:x is a vowel}, B = {x:x is a letter in the word "little"}, C = {x:x precedes f in the alphabet}, D = {x: x is a letter in the word "title"}