INFO 150: A Mathematical Foundation for Informatics

First Midterm Exam

David Mix Barrington

15 October 2017

Directions:

  Q1: 15 points
  Q2: 25 points
  Q3: 20 points
  Q4: 20 points
  Q5: 20 points
Total: 100 points

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

  • Question 2 (25): Translate these five statements as indicated. We have a set of dogs D including (among others) the named dogs Cardie, Duncan, Mia and Whistle who are denoted symbolically by c, d, m and w respectively. If x is a dog, the predicate PB(x) means "x belongs to Professor Barrington" and PG(x) means "x belongs to Professor Gill". We also have a set B of breeds, a predicate I(x, y) meaning "dog x is of breed y", and a predicate SB(x, y) meaning "dog x and dog y are of the same breed". Variables in quantifiers are of type "dog" or of type "breed" -- you can tell which by how they are used in predicates.

  • Question 3 (20): Prove the following using truth tables:

  • Question 4 (20): Prove the following statement:

  • Question 5 (20):

    Last modified 22 October 2017