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, The water not being cold is sufficient for going swimming. Having goggles is necessary for going swimming. I have no goggles. Therefore, the water is cold. Approach: Separate the premises from the conclusion. Major premise is the water not being cold is sufficient for going swimming. Minor premise is having goggles is necessary for going swimming and I have no goggles. Conclusion is the water is cold. The argument contains three simple statements of the form, p : The water is cold. q : I go swimming. r : I have goggles. Symbolically argument can be written in the form, Major premise: ∼ p → q Minor premise 1: q → r Minor premise 2: ∼ r Conclusion: p The premise 2 is, q → r And, The premise 3 is, ∼ r Apply modus tollens proof of validity in premise 2 and 3. The conclusion is ∼ q which is statement 4. The premise 1 is, ∼ p → q Apply transposition proof of validity in premise 1. The conclusion is ∼ q → ∼ ∼ p which is statement 5

8th Edition

ISBN: 8220100546112

Author: MOWRY

Publisher: Cengage Learning US

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Chapter 1.6, Problem 29E

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The formal proof of validity for the given argument.

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Chapter 1.6, Problem 28E

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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.