Explanation Given: The given argument is, Not investing money in the stock market is necessary for invested money to be guaranteed. Invested money not being guaranteed is sufficient for not retiring at an early age. Therefore, you retire at an early age only if your money is not invested in the stock market. Description: The disjunction p ∨ q joins the two statements with the word “or”. The disjunction is true if at least one of the components of the disjunction is true. The disjunction is false if both the statements are false. The conjunction p ∧ q joins the two statements with the word “and”. The conjunction is true if both the components of the conjunction is true. The conjunction is false if at least one of the statements is false. The conditional statement p → q is made up of two statements p and q . It follows the form “If p , then q ”. If the statement p is true the conditional statement will depend on whether the statement q is true or false. If the statement p is false the conditional statement will be false and does not depend on whether the statement q is true or false. The negation ∼ p is the opposite of the statement p . If the component of the statement is true the negation of statement is false and vice-versa. Approach: In the given statement, Not investing money in the stock market is necessary for invested money to be guaranteed. Invested money not being guaranteed is sufficient for not retiring at an early age. Therefore, you retire at an early age only if your money is not invested in the stock market. p : You are investing in the stock market. q : The invested money is to be guaranteed. r : You retire at an early age. Premise 1 is “Not investing money in the stock market is necessary for invested money to be guaranteed” that can be rephrased as “If invested money is to be guaranteed, it should not be invested in the stock market.” The symbolic form of premise 1 is q → ∼ p . Premise 2 is “Invested money not being guaranteed is sufficient for not retiring at an early age.” that can be rephrased as “If the invested money is not guaranteed then you cannot retire in an early age.” The symbolic form of premise 2 is ∼ q → ∼ r . Conclusion is “Therefore, you retire at an early age only if your money is not invested in the stock market.” The symbolic form of conclusion is r → ∼ p . The symbolic form of the given argument is, q → ∼ p ∼ q → ∼ r _ r → ∼ p The given argument is represented by the conditional [ ( q → ∼ p ) ∧ ( ∼ q → ∼ r ) ] → ( r → ∼ p )

8th Edition

ISBN: 9781305104174

Author: David B. Johnson, Thomas A. Mowry

Publisher: Cengage Learning

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Chapter 1.CR, Problem 65CR

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The validity of the given argument by using truth table.

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Chapter 1.CR, Problem 64CR

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