# MaThematics Essay Samples and Topic Ideas

Mathematics Page 42 1. List the (distinct) elements in each of the following sets: {x Z | xy = 15 for y Z}Solution: C = { 1, 3, 5, 15, -1, -3, -5, -15} (both positive and negative of 15) e. {a N | a <-4 and a >a} Solution:It is impossible to list the elements since they are infinite in number. āNā refers to natural numbers and therefore "-4" is irrelevant. 2. List five elements in each of the following sets: d. {nN|n2 + n is a multiple of 3} Solution:The numbers are in the form n2+n=3p for some integer P hence: n={3,5,6,8,9} 9a. List all the subsets of the set {a, b, c, d} that contain Solution i.) four elements - {a,b,c,d}ii.) three elements - {a,b,c}, {a,b,d}, {a,c,d}, {b,c,d}iii.) two...