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Construct a formal proof of validity. Represent the propositions using the suggested letters.

Construct a formal proof of validity. Represent the propositions using the suggested letters.

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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dia If Mr. Jones is the manager's next-door neighbor, then Mr. Jones's annual earnings are exactly divisible by 3. If Mr. Jones's annual earnings are exactly divisible by 3, then $40,000 is exactly divisible by 3. But $40,000 is not exactly divisible by 3. If Mr. Robinson is the manager's next-door neighbor, then Mr. Robinson lives halfway between Detroit and Chicago. If Mr. Robinson lives in Detroit, then he does not live halfway between Detroit and Chicago. Mr. Robinson lives in Detroit. If Mr. Jones is not the manager's next-door neighbor, then either Mr. Robinson or Mr. Smith is the manager's next-door neighbor. Therefore Mr. Smith is the manager's next-door neighbor. J--Mr. Jones is the manager's next-door neighbor; E--Mr. Jones's annual earnings are exactly divisible by 3; T--$40,000 is exactly divisible by 3; R--Mr. Robinson is the manager's next-door neighbor; H--Mr. Robinson lives halfway between Detroit and Chicago; D--Mr. Robinson lives in Detroit; S--Mr. Smith is the manager's next-door neighbor.
Transcribed Image Text:dia If Mr. Jones is the manager's next-door neighbor, then Mr. Jones's annual earnings are exactly divisible by 3. If Mr. Jones's annual earnings are exactly divisible by 3, then $40,000 is exactly divisible by 3. But $40,000 is not exactly divisible by 3. If Mr. Robinson is the manager's next-door neighbor, then Mr. Robinson lives halfway between Detroit and Chicago. If Mr. Robinson lives in Detroit, then he does not live halfway between Detroit and Chicago. Mr. Robinson lives in Detroit. If Mr. Jones is not the manager's next-door neighbor, then either Mr. Robinson or Mr. Smith is the manager's next-door neighbor. Therefore Mr. Smith is the manager's next-door neighbor. J--Mr. Jones is the manager's next-door neighbor; E--Mr. Jones's annual earnings are exactly divisible by 3; T--$40,000 is exactly divisible by 3; R--Mr. Robinson is the manager's next-door neighbor; H--Mr. Robinson lives halfway between Detroit and Chicago; D--Mr. Robinson lives in Detroit; S--Mr. Smith is the manager's next-door neighbor.
Instructions Construct a formal proof of validity. Represent the propositions using the suggested letters.
Transcribed Image Text:Instructions Construct a formal proof of validity. Represent the propositions using the suggested letters.
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