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Consider the statement, For all graphs G, if G contains an odd cycle, then x(G) > 3. Note, you do not need to know anything about graphs to answer these questions. What would the first line of a direct proof be? A. Assume there is a graph G which contains an odd cycle but for which x(G) < 3. O B. Let G be a graph and assume x(G) > 3. C. Let G be a graph and assume it contains an odd cycle. D. Let G be a graph and assume x(G) < 3. O E. Let G be a graph and assume it contains no odd cycles. What would the first line of a proof by contrapositive be? A. Let G be a graph and assume x(G) < 3. B. Assume there is a graph G which contains an odd cycle but for which x(G) < 3. O C. Let G be a graph and assume it contains an odd cycle. D. Let G be a graph and assume x(G) 2 3. E. Let G be a graph and assume it contains no odd cycles. What would the first line of a proof by contradiction be? O A. Assume there is a graph G which contains an odd cycle but for which x(G) < 3. B. Let G be a graph and assume x(G) < 3. C. Let G be a graph and assume it contains an odd cycle. D. Let G be a graph and assume it contains no odd cycles. E. Let G be a graph and assume x(G) > 3.

Consider the statement, For all graphs G, if G contains an odd cycle, then x(G) > 3. Note, you do not need to know anything about graphs to answer these questions. What would the first line of a direct proof be? A. Assume there is a graph G which contains an odd cycle but for which x(G) < 3. O B. Let G be a graph and assume x(G) > 3. C. Let G be a graph and assume it contains an odd cycle. D. Let G be a graph and assume x(G) < 3. O E. Let G be a graph and assume it contains no odd cycles. What would the first line of a proof by contrapositive be? A. Let G be a graph and assume x(G) < 3. B. Assume there is a graph G which contains an odd cycle but for which x(G) < 3. O C. Let G be a graph and assume it contains an odd cycle. D. Let G be a graph and assume x(G) 2 3. E. Let G be a graph and assume it contains no odd cycles. What would the first line of a proof by contradiction be? O A. Assume there is a graph G which contains an odd cycle but for which x(G) < 3. B. Let G be a graph and assume x(G) < 3. C. Let G be a graph and assume it contains an odd cycle. D. Let G be a graph and assume it contains no odd cycles. E. Let G be a graph and assume x(G) > 3.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Consider the statement, For all graphs G, if G contains an odd cycle, then x(G) > 3. Note, you do not need to know anything about graphs to answer these questions. What would the first line of a direct proof be? A. Assume there is a graph G which contains an odd cycle but for which x(G) < 3. O B. Let G be a graph and assume x(G) > 3. O C. Let G be a graph and assume it contains an odd cycle. O D. Let G be a graph and assume x(G) < 3. O E. Let G be a graph and assume it contains no odd cycles. What would the first line of a proof by contrapositive be? O A. Let G be a graph and assume x(G) < 3. O B. Assume there is a graph G which contains an odd cycle but for which x(G) < 3. O C. Let G be a graph and assume it contains an odd cycle. D. Let G be a graph and assume x(G) > 3. O E. Let G be a graph and assume it contains no odd cycles. What would the first line of a proof by contradiction be? A. Assume there is a graph G which contains an odd cycle but for which x(G) < 3. O B. Let G be a graph and assume x(G) < 3. C. Let G be a graph and assume it contains an odd cycle. O D. Let G be a graph and assume it contains no odd cycles. O E. Let G be a graph and assume x(G) > 3.
Transcribed Image Text:Consider the statement, For all graphs G, if G contains an odd cycle, then x(G) > 3. Note, you do not need to know anything about graphs to answer these questions. What would the first line of a direct proof be? A. Assume there is a graph G which contains an odd cycle but for which x(G) < 3. O B. Let G be a graph and assume x(G) > 3. O C. Let G be a graph and assume it contains an odd cycle. O D. Let G be a graph and assume x(G) < 3. O E. Let G be a graph and assume it contains no odd cycles. What would the first line of a proof by contrapositive be? O A. Let G be a graph and assume x(G) < 3. O B. Assume there is a graph G which contains an odd cycle but for which x(G) < 3. O C. Let G be a graph and assume it contains an odd cycle. D. Let G be a graph and assume x(G) > 3. O E. Let G be a graph and assume it contains no odd cycles. What would the first line of a proof by contradiction be? A. Assume there is a graph G which contains an odd cycle but for which x(G) < 3. O B. Let G be a graph and assume x(G) < 3. C. Let G be a graph and assume it contains an odd cycle. O D. Let G be a graph and assume it contains no odd cycles. O E. Let G be a graph and assume x(G) > 3.
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