Consider the conditional statement: If a graph is connected, has n vertices, and has n-1 edges, then the graph has no circuits. Write the following variations of the conditional as English language statements (do not answer in formal notation): 1. Converse 2. Inverse 3. Contrapositive 4. Negation
Consider the conditional statement: If a graph is connected, has n vertices, and has n-1 edges, then the graph has no circuits. Write the following variations of the conditional as English language statements (do not answer in formal notation): 1. Converse 2. Inverse 3. Contrapositive 4. Negation
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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1. The converse of P→ 9 is db d .
Converse: If a graph has no circuits, then it is connected and has n vertices and n edges.
2. The inverse of P→ 9 is b nk d~ 9 .
Inverse: If a graph is not connected or doesn't have n vertices and n edges, then the graph has a circuit.
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3. The contrapositive of P→ 9 is \sim q\to \sim p.
Contrapositive: If a graph has a circuit, then it is either not connected or doesn't have n vertices and n edges.
4. The negation of P→ 9 is b~ vd b .
Negation: A graph is connected and has n vertices and n edges and also has a circuit.
Transcribed Image Text:Consider the conditional statement:
If a graph is connected, has n vertices, and has n-1 edges, then the graph has no circuits.
Write the following variations of the conditional as English language statements (do not answer in
formal notation):
1. Converse
2. Inverse
3. Contrapositive
4. Negation
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