# Natural Essay Examples

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 elements - {a,b}, {a,c}, {a,d}, {b,c}, {b,d}, {c,d}iv.) one element - {a}, {b}, {c}, {d}v.) no elements - {0} Page 49 3. Let A = {(-1,2), (4, 5), (0, 0), (6, -5), (5, 1), (4, 3)}. a. {a + b | (a, b) A} Solution: A = {1, 9, 0, 6, 7}. b. {a | a >0 and (a, b) A for some b} Solution:{4,6,5,4} 4. List the elements in the...