CMPSCI 250: Introduction to Computation

Solutions to Final Exam Fall 2018

David Mix Barrington and Marius Minea

Exam given 20 December 2018

Solutions posted 31 December 2018


Question text is in black, solutions in blue.

  Q1: 30 points
  Q2: 30 points
  Q3: 30+10 points
  Q4: 30 points
Total: 120+10 points

Here are definitions of some terms, sets, predicates, and statements used on this exam.

Question 1 deals with the following scenario:

During one cold week in December, each dog in the set S = {c, d, n, p} = {Cardie, Duncan, Nina, Pushkin} went for a walk on each day in the set Y = {Mon, Tue, Wed, Thu, Fri}. On each day, each dog chose whether to wear a coat, based on the temperature that morning.

Let Z be the set of integers {..., -3, -2, -1, 0, 1, 2, 3,...}. Let f be the function from S to Z defined so that f(x) is the "critical temperature" (in Celsius) for dog x: the meaning of this will come from Statement I below. Let t be the function from Y to Z defined so that t(y) is the outdoor temperature, in Celsius, on the morning of day y. Let W be the predicate defined so that W(x, y) means "dog x wore a coat on day y".

Question 1 also refers to the following four statements, where the variables are of type "dog", type "day", or type "integer":

The statements are:

N is the set of naturals (non-negative integers, {0, 1, 2, 3,...}.

The Koch snowflake is obtained by recursively defining the polygons Sn in the following way:

Last modified 2 January 2019