CMPSCI 190DM: A Mathematical Foundation for Informatics

Practice for Third Midterm Exam

David Mix Barrington

12 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. No explanation is needed or wanted, and there is no penalty for guessing.

  • Question 3 (35): Let X be the set of dogs {Arly, Baxter, Cardie, Duncan, Ebony}. 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, and C be any three sets. Give an element-wise proof that (A - B) ∪ (B - C) ⊆ (B ∩ C)'. (Recall that if X and Y are any two sets, Y' is the complement of Y and "X - Y" means "(X ∩ Y')".)

  • Question 5 (20): Let f: A → B and g: B → C be two functions that are each bijections. Let h: A → C be defined so that for any x in A, h(x) = g(f(x)). Prove that h is a bijection. (Recall that a function is a bijection if and only if it is both one-to-one and onto.)

    Last modified 12 November 2015