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04-BS-16: May 2013

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

  1. Question 1 Logic — Propositions, Compound Propositions and Quantifiers
  2. Question 2 Mathematical Induction
  3. Question 3 Pigeonhole and Induction Proofs
  4. Question 4 Power Sets, Partitions, and Set-Builder Families
  5. Question 5 Relations — Reflexive, Symmetric, Antisymmetric, Transitive
  6. Question 6 Algorithm Analysis and Big-O Notation
  7. Question 7 Permutations, Combinations, and Multiset Arrangements
  8. Question 8 Discrete Probability — Dice and Seating
  9. Question 9 Pigeonhole (Ramsey R(3,3)) and Inclusion-Exclusion
  10. Question 10 Graph Theory — Paths, Planarity, Algorithms, Colouring
  11. Question 11 Euler's Formula for Planar Graphs and Polyhedra
  12. Question 12 Conditional Probability and the Binomial Distribution

Start with Question 1 →

National Examination, 04-BS-16 Discrete Mathematics, May 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, induction & recursion Ch.5, counting Ch.6, discrete probability Ch.7, relations Ch.9, graphs Ch.10-11); Epp, Discrete Mathematics with Applications.