MATH 2030 Final: MATH 2030 University of Manitoba MATH2030 Final Exam Draft

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Signature: (in ink) (i understand that cheating is a serious o ense) Please show your work clearly and justify all answers. No texts, notes, or other aids are permitted. There are no calculators, cellphones or electronic translators permitted. This exam has a title page, 15 pages of questions and also 1 blank page for rough work. Please check that you have all the pages. The value of each question is indicated in the left hand margin beside the statement of the question. Answer all questions on the exam paper in the space provided beneath the question. If you need more room, you may continue your work on the reverse side of the page, but clearly indicate that your work is continued. A binary relation (x, r) is anti-symmetric if. A binary relation (x, r) is asymmetric if. A binary relation (x, r) is negatively transitive if. A strict partial order (x, r) is a lattice if.