Explanation Given: The given proposition is “If Lehman Brothers was no longer able to pay out on the losing bets that it had made. [Then] somebody else suddenly had hole in his portfolio” – Nate Silver, the signal and the Noise a) Consider the following statement by Nate Silver from The Signal. “If a Lehman brother was no longer able to pay out on the losing bets that bets that it had made, then somebody else suddenly had a huge hole in his portfolio”. The statement is of the form if p, then q with the proposition p as “Lehman Brothers was no longer able to pay out on the losing bets that it had made” and q as “somebody else suddenly had a huge in his portfolio” If the proposition p is true, that is, if Lehman Brothers cannot pay out on its losing bets, then the logical conclusion that it follows is that q is also true. So it can be concluded that ‘somebody has a huge in his portfolio’. b) The statement is of form if p, then q with the proposition p as “Lehman Brothers was no longer able to pay out on the losing bets that it had made” and q as “somebody else suddenly had a huge hole in his portfolio.” In a conditional proposition of the form if p, then q, q is a necessary for p however p is a sufficient for q. So if q not true, then it can be safely concluded that p is not true. Therefore, if it is said that ‘no one has a huge in his portfolio’, then the logical conclusion will be “Lehman Brothers was able to pay out on its losing bets” c) As done in part (b) the conclusion that Lehman Brothers does day out on its losing bets can be made given no one else has a huge hole in his portfolio...

Using and Understanding Mathematics: A Quantitative Reasoning Approach (6th Edition)

6th Edition

ISBN: 9780321914620

Author: Jeffrey O. Bennett, William L. Briggs

Publisher: PEARSON

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Chapter 1.D, Problem 63E

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Consider the following propositions, and answer the question that follows.

a) What is the logical conclusion (if any) in the event that Lehman Brothers cannot pay out on its losing bets?

b) What is the logical conclusion (if any) in the event that no one has a huge hole in his portfolio?

c) Can you draw any conclusion about what happens if Lehman Brothers cannot pay out on its losing bets?

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Chapter 1.D, Problem 62E

Chapter 1.D, Problem 64E

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Chapter 1 Solutions

Using and Understanding Mathematics: A Quantitative Reasoning Approach (6th Edition)

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