Explanation The following are the steps of a formal proof of validity for an argument, 1. Number the premises in a column. 2. Skip conclusion numbering and continue the numbering of remaining premises. 3. Apply an elementary valid argument form on the selected two premises. 4. Put this new statement in the original numbered column and write its justification to its right. The justification includes the numbers of two statements and the abbreviation of the elementary valid argument form. Given: The given arguments is, Drinking espresso is sufficient for not sleeping. Not eating dessert is necessary for being on a diet. Not eating dessert is sufficient for drinking espresso. Therefore, not being on a diet is necessary for sleeping. Approach: Separate the premises from the conclusion. Major premise is Drinking espresso is sufficient for not sleeping. Minor premise is not eating dessert is necessary for being on a diet and not eating dessert is sufficient for drinking espresso. Conclusion is not being on a diet is necessary for sleeping. The argument contains three simple statements of the form, p : Drinking Espresso. q : Sufficient for sleeping. r : Eating Desert. s: Being on a diet. Symbolically argument can be written in the form, Major premise: p → ∼ q Minor premise 1: s → ∼ r Minor premise 2: ∼ r → p Conclusion: q → ∼ s The premise 2 is, s → ∼ r And, The premise 3 is, ∼ r → p Apply hypothetical syllogism proof of validity in premise 2 and 3. The conclusion is s → p which is statement 4. The premise 4 is, s → p Apply transposition proof of validity in premise 4. The conclusion is ∼ p → ∼ s which is statement 5

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ISBN: 8220100546112

Author: MOWRY

Publisher: Cengage Learning US

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Chapter 1.6, Problem 28E

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The formal proof of validity for the given argument.

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Chapter 1.6, Problem 27E

Chapter 1.6, Problem 29E

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To construct: The formal proof of validity for the given argument.

Solution Summary: The author explains the steps of a formal proof of validity for an argument.