Question

Which of the following proper subsets of R contain their suprema but do not contain their infinima? 6 Multiple answers: You can select more than one option OA (a:b B (a,b) union with (a-10,b-10] Oc(5:15) O D (-5:16) union with [5:10] OE (-6,3] intersected with (2,5)

Answer 1

Suprema = least upper bound infinima = greatest lower bound A = [a, b] Rightarrow suprema = b elementof [a, b] infinima = a Notelement [a, b] Rightarrow A contains suprema but not infinima B = [a, b] Union (a - 10, b - 10) = (a - 10, b) Rightarrow suprema = b Notelement B infinima = a - 10 Notelement B Rightarrow B close not contain both its suprema and infinima c = [5, 15) Righarrow suprema = 15 Notelement C infinima = 5 elementof c Rightarrow C contain its infinima but not suprema D = (-5, 16) Union [5, 10] = (-5, 16) Rightarrow suprema = 16 Notelement D infinima = -5 Notelement D Rightarrow D dose not contain both infinima and suprema E = [-6, 3] Intersection [2, 5] = [2, 3] Rightarrow suprema = 3 elementof E infinima = 2 elementof E Rightarrow E contains both suprema and infinima