WGU C959 MATH 2800 Discrete Mathematics Comprehensive OA

WGU C959 MATH 2800 Discrete Mathematics


Comprehensive OA



C959 MATH 2800



Discrete Mathematics I



Comprehensive Objective Assessment



2025/2026


INTRODUCTION:



This document is a complete study resource for the WGU course C959
MATH 2800 Discrete Mathematics I. It contains the full set of
questions and correct answers for the Comprehensive Objective
Assessment (OA) for the 2025/2026 academic year. The material
covers all key topics in discrete mathematics, including sets, logic,

,relations, functions, graph theory, combinatorics, and algorithms. It
is a fully detailed exam preparation file that aligns directly with the
WGU assessment format.




EXAMS QUESTIONS AND ANSWERS:



17. Multiple Choice Question

Which of these relationships about the number of edges e, the
number of vertices v, and the number of regions r in a planar graph
is correct?--- correct answer --- r = e - v + 2

18. Matching Question

Match each characterization of a connected planar simple graph
hand column with the number of regions such a graph splits in t the
right hand column.--- correct answer ---

19. Fill in the Blank Question

The operation on a simple graph of removing an edge {u, v} and
then adding a new vertex w together with new edges {u, w} and {w,
v} is called (BLANK 1) subdivision. Two graphs are called (BLANK
2) if they can be obtained from the same graph by a sequence of
such operations.--- correct answer --- Blank 1--- correct answer ---
elementary

Blank 2--- correct answer --- homeomorphic

20. Question Mode Multiple Select Question Select all that apply

,Which of these statements about planar graphs are true?--- correct
answer --- There are 10 regions in a planar

representation of a graph with 20 edges and 12 vertices.

A connected planar simple graph with 15 vertices and 16 edges
could be planar.

21. Question Mode Multiple Choice Question

Which of these criteria can be used to show that K3,3 is nonplanar?-
-- correct answer --- If a connected planar simple graph has e edges
and v vertices, where v e3, and no circuits of length 3, then e d2v -
4.

22. Multiple Select Question Select all that apply

Which of these statements are true about the dual graph of a planar
map?--- correct answer --- Each

region of the map is represented by a vertex.

Two vertices of the dual graph are connected by an edge if the
regions they represent have a common border.

The dual graph is planar.

23. Multiple Select Question Select all that apply

Kuratowski's theorem says that a graph is nonplanar if it contains a
subgraph homeomorphic to which of these graphs? (Select all that
apply.)--- correct answer --- K5

K3,3

24. Fill in the Blank Question

, A coloring of a simple graph is the assignment of a color to each
vertex so that no two adjacent vertices are assigned the same color.
The (BLANK 1) number of a graph is the least number of colors
needed for a coloring of the graph.--- correct answer --- Blank 1---
correct answer --- chromatic

25. Question Mode Ordering Question

Click and drag on elements in order

Construct a proof that every planar simple graph has a vertex of
exceeding five.--- correct answer ---

1. Multiple Choice Question

Which of these provides a correct analysis of the famous
Köningsberg bridge problem?--- correct answer --- The bridges
multigraph has four odd vertices, so it has no Euler circuit. Thus
one cannot cross each bridge exactly once and return to the start.

2. Question Mode Multiple Select Question Select all that apply

Which of these are applications of Euler paths or circuits?---
correct answer --- Finding a route for a postman

so that the route covers each street in the route exactly once



Finding a route for a snowplow that traverses each street in the
route exactly once

3. Fill in the Blank Question

A simple path in a graph G passing through all vertices in the graph
exactly once is called a (BLANK 1) path.--- correct answer --- Blank
1--- correct answer --- Hamilton or Hamiltonian