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In 13-18 determine whether each sentence is a statement. Explain your answers. 19. a. Assuming that the following sentence is a statement, prove that 1+1 = 3: If this sentence is true, then 1+1 = 3. b. What can you deduce from part (a) about the status of "This sentence is true"? Why? (This example is known as Löb's paradox.)

In 13-18 determine whether each sentence is a statement. Explain your answers. 19. a. Assuming that the following sentence is a statement, prove that 1+1 = 3: If this sentence is true, then 1+1 = 3. b. What can you deduce from part (a) about the status of "This sentence is true"? Why? (This example is known as Löb's paradox.)

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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In 13-18 determine whether each sentence is a statement. Explain your answers.
Transcribed Image Text:In 13-18 determine whether each sentence is a statement. Explain your answers.
19. a. Assuming that the following sentence is a statement, prove that 1+1 = 3: If this sentence is true, then 1+1 = 3. b. What can you deduce from part (a) about the status of "This sentence is true"? Why? (This example is known as Löb's paradox.)
Transcribed Image Text:19. a. Assuming that the following sentence is a statement, prove that 1+1 = 3: If this sentence is true, then 1+1 = 3. b. What can you deduce from part (a) about the status of "This sentence is true"? Why? (This example is known as Löb's paradox.)
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