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04-BS-16: December 2013

Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)

  1. Question 1 Logic — Quantified Statements and Predicates
  2. Question 2 Sets — Union, Intersection, Cartesian Product, Power Set
  3. Question 3 Induction and Pigeonhole Proofs
  4. Question 4 Relations — Divisibility on a Finite Set and on the Positive Integers
  5. Question 5 Functions — Domain, Range, Injectivity, Surjectivity, Invertibility
  6. Question 6 Counting — Multiset Permutations and Stars-and-Bars
  7. Question 7 Discrete Probability — Dice and Conditional Probability
  8. Question 8 Algorithm Analysis, Big-O, and Growth-Rate Ordering
  9. Question 9 Graph Theory — Euler Paths and Planarity
  10. Question 10 Insertion Sort — Best, Worst, and Big-O Complexity
  11. Question 11 Euler's Polyhedron Formula
  12. Question 12 Chromatic Number and Graph-Colouring Scheduling

Start with Question 1 →

National Examination, 04-BS-16 Discrete Mathematics, Dec 2013. Closed book, no aids, 3 hours, 12 questions of 10 marks each (100 marks); the exam instructs "answer 10 of 12" but every question is solved below as a complete study resource.

Reference texts: Rosen, Discrete Mathematics and Its Applications, 7th ed. (logic Ch.1, sets Ch.2, induction & pigeonhole Ch.5-6, relations Ch.9, counting Ch.6, discrete probability Ch.7, graphs Ch.10-11); Epp, Discrete Mathematics with Applications.