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WGU C960: Discrete Math II|OA| EXAM WITH COMPLETE 250
REAL EXAM QUESTIONS AND CORRECT DETAILED
ANSWERS (VERIFIED ANSWERS) ALREADY GRADED A+
1. A relation RR on the set of integers is defined by aRbaRb if and only
if a−ba-b is divisible by 4. Which property does RR satisfy?
A. Reflexive but not symmetric
B. Symmetric but not transitive
C. Reflexive, symmetric, and transitive
D. Irreflexive and transitive
Answer: C
2. Consider the recurrence relation an=3an−1−2a_n=3a_{n-1}-2 with
a1=4a_1=4. Which expression gives the closed form for ana_n?
A. 3n+23^n+2
B. 3n−1+13^{n-1}+1
C. 2(3n)−12(3^n)-1
D. 3n−1+33^{n-1}+3
Answer: B
3. A graph contains 10 vertices, each having degree 4. How many edges
does the graph contain?
A. 20
B. 40
C. 10
D. 80
Answer: A
4. Which statement must be true for every finite undirected graph?
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A. Every vertex has an even degree.
B. The number of vertices with odd degree is even.
C. The graph must contain a Hamiltonian cycle.
D. The graph must be connected.
Answer: B
5. A connected graph has exactly two vertices of odd degree. Which
conclusion follows from Euler's theorem?
A. It contains an Euler circuit.
B. It contains an Euler path but not an Euler circuit.
C. It contains neither an Euler path nor an Euler circuit.
D. It must contain a Hamiltonian cycle.
Answer: B
6. A graph has vertices A,B,C,D,EA,B,C,D,E and edges
AB,BC,CD,DE,EAAB, BC, CD, DE, EA. Which statement correctly
describes the graph?
A. It is a complete graph K5K_5.
B. It is a path graph with five vertices.
C. It is a cycle graph C5C_5.
D. It is a tree.
Answer: C
7. A connected simple graph has 12 vertices and 11 edges. Which
conclusion is necessarily correct?
A. The graph contains exactly one cycle.
B. The graph is a tree.
C. Every vertex has degree 2.
D. The graph must be complete.
Answer: B
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8. A tree has 15 vertices. How many edges must it have?
A. 14
B. 15
C. 16
D. 30
Answer: A
9. A complete graph K7K_7 is given. How many edges does it contain?
A. 14
B. 21
C. 28
D. 42
Answer: B
10. A planar connected graph has V=8V=8 vertices and E=12E=12
edges. Using Euler's formula V−E+F=2V-E+F=2, how many faces does
the graph have, including the exterior face?
A. 4
B. 5
C. 6
D. 7
Answer: C
11. Which condition is sufficient to establish that a graph has an Euler
circuit?
A. Every vertex has odd degree and the graph is connected.
B. The graph is connected and every vertex has even degree.
C. The graph contains exactly two odd-degree vertices.
D. The graph is acyclic.
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Answer: B
12. A Hamiltonian cycle differs from an Euler circuit because a
Hamiltonian cycle:
A. Must use every edge exactly once.
B. Must visit every vertex exactly once before returning to the starting
vertex.
C. Can contain repeated vertices.
D. Exists only in directed graphs.
Answer: B
13. A connected weighted graph has edges with weights representing
transportation costs. Which algorithm is specifically designed to
determine a minimum spanning tree?
A. Dijkstra's algorithm
B. Prim's algorithm
C. Floyd-Warshall algorithm
D. Breadth-first search
Answer: B
14. A network contains the following weighted edges: AB=2AB=2,
AC=5AC=5, BC=1BC=1, BD=4BD=4, CD=3CD=3. Which set of edges
can form a minimum spanning tree?
A. AB,AC,BDAB, AC, BD
B. AB,BC,CDAB, BC, CD
C. AC,BC,BDAC, BC, BD
D. AC,BD,CDAC, BD, CD
Answer: B
15. Dijkstra's algorithm is most appropriately used to:
WGU C960: Discrete Math II|OA| EXAM WITH COMPLETE 250
REAL EXAM QUESTIONS AND CORRECT DETAILED
ANSWERS (VERIFIED ANSWERS) ALREADY GRADED A+
1. A relation RR on the set of integers is defined by aRbaRb if and only
if a−ba-b is divisible by 4. Which property does RR satisfy?
A. Reflexive but not symmetric
B. Symmetric but not transitive
C. Reflexive, symmetric, and transitive
D. Irreflexive and transitive
Answer: C
2. Consider the recurrence relation an=3an−1−2a_n=3a_{n-1}-2 with
a1=4a_1=4. Which expression gives the closed form for ana_n?
A. 3n+23^n+2
B. 3n−1+13^{n-1}+1
C. 2(3n)−12(3^n)-1
D. 3n−1+33^{n-1}+3
Answer: B
3. A graph contains 10 vertices, each having degree 4. How many edges
does the graph contain?
A. 20
B. 40
C. 10
D. 80
Answer: A
4. Which statement must be true for every finite undirected graph?
,2|Page
A. Every vertex has an even degree.
B. The number of vertices with odd degree is even.
C. The graph must contain a Hamiltonian cycle.
D. The graph must be connected.
Answer: B
5. A connected graph has exactly two vertices of odd degree. Which
conclusion follows from Euler's theorem?
A. It contains an Euler circuit.
B. It contains an Euler path but not an Euler circuit.
C. It contains neither an Euler path nor an Euler circuit.
D. It must contain a Hamiltonian cycle.
Answer: B
6. A graph has vertices A,B,C,D,EA,B,C,D,E and edges
AB,BC,CD,DE,EAAB, BC, CD, DE, EA. Which statement correctly
describes the graph?
A. It is a complete graph K5K_5.
B. It is a path graph with five vertices.
C. It is a cycle graph C5C_5.
D. It is a tree.
Answer: C
7. A connected simple graph has 12 vertices and 11 edges. Which
conclusion is necessarily correct?
A. The graph contains exactly one cycle.
B. The graph is a tree.
C. Every vertex has degree 2.
D. The graph must be complete.
Answer: B
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8. A tree has 15 vertices. How many edges must it have?
A. 14
B. 15
C. 16
D. 30
Answer: A
9. A complete graph K7K_7 is given. How many edges does it contain?
A. 14
B. 21
C. 28
D. 42
Answer: B
10. A planar connected graph has V=8V=8 vertices and E=12E=12
edges. Using Euler's formula V−E+F=2V-E+F=2, how many faces does
the graph have, including the exterior face?
A. 4
B. 5
C. 6
D. 7
Answer: C
11. Which condition is sufficient to establish that a graph has an Euler
circuit?
A. Every vertex has odd degree and the graph is connected.
B. The graph is connected and every vertex has even degree.
C. The graph contains exactly two odd-degree vertices.
D. The graph is acyclic.
, 4|Page
Answer: B
12. A Hamiltonian cycle differs from an Euler circuit because a
Hamiltonian cycle:
A. Must use every edge exactly once.
B. Must visit every vertex exactly once before returning to the starting
vertex.
C. Can contain repeated vertices.
D. Exists only in directed graphs.
Answer: B
13. A connected weighted graph has edges with weights representing
transportation costs. Which algorithm is specifically designed to
determine a minimum spanning tree?
A. Dijkstra's algorithm
B. Prim's algorithm
C. Floyd-Warshall algorithm
D. Breadth-first search
Answer: B
14. A network contains the following weighted edges: AB=2AB=2,
AC=5AC=5, BC=1BC=1, BD=4BD=4, CD=3CD=3. Which set of edges
can form a minimum spanning tree?
A. AB,AC,BDAB, AC, BD
B. AB,BC,CDAB, BC, CD
C. AC,BC,BDAC, BC, BD
D. AC,BD,CDAC, BD, CD
Answer: B
15. Dijkstra's algorithm is most appropriately used to:
