Discrete Mathematics Exam 2 - Fall '03 by Prof. S. Brick, Exams of Discrete Mathematics

Download Discrete Mathematics Exam 2 - Fall '03 by Prof. S. Brick and more Exams Discrete Mathematics in PDF only on Docsity! Prof. S. Brick Math 267 Fall ’03 Discrete Math; Exam 2 section 101 Print your name: Directions: Show all of your work, and explain your reasoning. 1. Prove by induction that in any tree we have V −E = 1 where V is the number of vertices and E is the number of edges. 2. Let S be the set of ternary strings (i.e., over {0, 1, 2}) of length 2 and f : S → N be the function f(a1a2) = a1 + a2. Find the partition induced by the kernel relation of f . 3. Find three different topological sortings of the poset with Hasse diagram: 4. Give a recursive definition for the reverse of a string. 5. Give an inductive definition of the set { x ∈ N | floor(x/2) is even } 6. Draw the Hasse diagram of the partial ordering on the set of positive divisors of 12 given by “evenly divides”.