Explanation Given: The given argument is, I will go to the concert only if you buy me a ticket. You bought me a ticket. Therefore, I will go to the concert. 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, I will go to the concert only if you buy me a ticket. You bought me a ticket. Therefore, I will go to the concert. p : I will go to a concert. q : You buy me a ticket. Premise 1 is “I will go to the concert only if you buy me a ticket.” The symbolic form of premise 1 is p → q . Premise 2 is “You bought me a ticket.” The symbolic form of premise 2 is q . Conclusion is “Therefore, I will go to the concert.” The symbolic form of conclusion is p . The symbolic form of the given argument is, p → q q _ p The given argument is represented by the conditional [ ( p → q ) ∧ q ] → p

Bundle: Mathematics: A Practical Odyssey, 8th + WebAssign Printed Access Card for Johnson/Mowry's Mathematics: A Practical Odyssey, 8th Edition, Single-Term

8th Edition

ISBN: 9781337349611

Author: David B. Johnson, Thomas A. Mowry

Publisher: Cengage Learning

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Chapter 1.CR, Problem 59CR

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The validity of the given argument by using truth table.

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The validity of the given argument by using truth table.

Solution Summary: The author explains how the truth table determines the validity of the given argument. The conditional statement pto q is made up of two statements.

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