INFO 150: A Mathematical Foundation for Informatics

Practice for First Midterm Exam

David Mix Barrington

5 October 2016

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 the following statements as indicated. The dogs Cardie, Duncan, and Mia are denoted symbolically by c, d, and m respectively. If x is a dog, the predicate B(x) means "x is barking". If is a dog and y is a number, the predicate A(x, y) means "dog x is age y". The symbols "<", "≤", "=", "≥", and ">" on numbers have their usual meaning.

  • Question 3 (20): Establish the following fact with truth tables:

  • Question 4 (20): Prove that for any number n, if n is the square of an even number and n > 10, then n - 1 is not a prime number.

  • Question 5 (20): Prove by induction on n that the number 7n - 1 is divisible by 6.

    Last modified 6 October 2016