CMPSCI 190DM: A Mathematical Foundation for Informatics

Third Midterm Exam

David Mix Barrington

18 November 2015


  Q1: 15 points
  Q2: 15 points
  Q3: 35 points
  Q4: 15 points
  Q5: 20 points
Total: 100 points

  • Question 1 (15): Briefly identify the following terms or concepts (3 points each):

  • Question 2 (15): Determine whether each of these five statements is true or false (3 points each). No explanation is needed or wanted, and there is no penalty for guessing. In the first three statements, A and B are finite sets and f: A → B is a function.

  • Question 3 (35): Let X be the set of dogs {Arly, Baxter, Cardie, Duncan}. Give the sizes of each of the following sets. No proof is necessary for a correct answer, but a justification may help with partial credit (5 points each).

  • Question 4 (15): Let A, B, C, and D be any four sets. Assume that A ⊆ B and that C ⊆ D. Give an element-wise proof that (A ∪ C) ⊆ (B ∪ D).

  • Question 5 (20): Let A, B, and C be finite sets with |A| > |B| and |A| = |C|. (Here "|X|" denotes the number of elements in X.) Let f: A → B and g: B → C be any two functions. Define h: A → C be defined by the rule h(a) = g(f(a)). Prove that h not a bijection.

    Last modified 19 November 2015