102_2017_3_b - MAT2612 Tutorial letter INTRODUCTION TO...

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BARCODE Define tomorrow. university of south africa Tutorial letter 102/3/2017 INTRODUCTION TO DISCRETE MATHEMATICS MAT2612 Semesters 1 & 2 Department of Mathematical Sciences ERRATA, THE EXAM AND SOLUTION OF OCTOBER 2016 EXAM PAPER MAT2612/102/3/2017
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Dear Student This tutorial letter contains the following information: 1. ERRATA IN THE PRESCRIBED BOOK 2. THE EXAM 3. THE OCTOBER/NOVEMBER 2016 EXAM PAPER AND SOLUTIONS 1. ERRATA IN THE 6 TH EDITION OF KBR (The following are correct in the 5 th edition.) p.491: Answers to Exercise 4.4 Some answers have been left out and the numbering is incorrect. Please change the numbers of the questions as follows: 17 19 (i.e. change 17 to 19) 19 21 21 23 23 25 25 27 27 29 29 31 31 33 33 35 35 37 37 39 Include the following answers: 13. reflexive 15. reflexive, antisymmetric, transitive 17. irreflexive, symmetric 2. THE EXAM The exam is two hours long and the paper counts out of 100 marks. Most questions will be similar to those asked in the self–evaluation tasks and assignments. You must know and be able to apply all definitions and statements of theorems. However, you need only know the proofs of the following theorems (YOU MAY BE ASKED TO PROVE ONE OF THE THEOREMS IN THE EXAM): Section 3.1: Theorems 3 and 4 Section 3.2: Theorem 1 Section 4.1: Theorem 1 Section 4.7: Theorem 8 2
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MAT2612/102/3/2017 Section 5.1: Theorem 4 Section 6.2: Theorems 1 and 2 Note that the proof of a theorem may be given before the statement of the theorem in KBR. You may also be asked to give a short proof of a statement by applying definitions and state- ments of theorems. You need not know the “Rules for Determining the Θ – Class of a Function” given on p. 203 (6 th edition of KBR), p. 186 (5 th edition of KBR). 3. THE OCTOBER/NOVEMBER 2016 EXAM PAPER AND SOLUTIONS This is the October/November 2016 exam paper. The best way to use this in your preparation for the exam, is the following: First, revise your work; try to do this exam without looking at the solutions or your textbook; and only then look at the answers. Good luck! MAT2612 October/November 2016 INTRODUCTION TO DISCRETE MATHEMATICS Duration : 2 Hours 100 Marks 1. Use mathematical induction to show that n ! > 2 n for all n N ; n 4 . [ 7 ] Let P ( n ) be the statement that n ! > 2 n .
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