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If you tell me the time, I'll pick you up at the airport. I pick you up at the airport. . You told me the time. Let p represent "You tell me the time." Let q represent "I pick you up at the airport." Select the correct choice below and fill in the answer box with the symbolic form of the argument.

If you tell me the time, I'll pick you up at the airport. I pick you up at the airport. . You told me the time. Let p represent "You tell me the time." Let q represent "I pick you up at the airport." Select the correct choice below and fill in the answer box with the symbolic form of the argument.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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### Translating Arguments into Symbolic Form This exercise involves translating a given argument into symbolic form and determining its validity. You may use a truth table or compare the argument's symbolic form to a standard valid or invalid form to accomplish this. #### Given Argument 1. If you tell me the time, I'll pick you up at the airport. 2. I pick you up at the airport. 3. Therefore, you told me the time. #### Translating the Argument Let: - \( p \) represent "You tell me the time." - \( q \) represent "I pick you up at the airport." In symbolic form, the argument is: 1. \( p \to q \) 2. \( q \) 3. \(\therefore p \) #### Determining the Validity Next, we determine whether the argument is valid or invalid by comparing it with standard forms: - **Valid Argument Form:** - Modus Ponens: - \( p \to q \) - \( p \) - \(\therefore q \) - Modus Tollens: - \( p \to q \) - \( \neg q \) - \(\therefore \neg p \) - **Invalid Argument Form:** - Affirming the Consequent: - \( p \to q \) - \( q \) - \(\therefore p \) (This is the form presented here.) #### Conclusion Select the correct option below: - \( \ \text{A.} \) The argument is valid. In symbolic form the argument is \( p \to q, q, \therefore p \) - \( \ \text{B.} \) The argument is invalid. In symbolic form the argument is \( p \to q, q, \therefore p \) Choose option: \( \text{B} \) ### Explanation of the Diagram There isn't a diagram or graph associated with this problem. The question is focused solely on logical reasoning and symbolic representation.
Transcribed Image Text:### Translating Arguments into Symbolic Form This exercise involves translating a given argument into symbolic form and determining its validity. You may use a truth table or compare the argument's symbolic form to a standard valid or invalid form to accomplish this. #### Given Argument 1. If you tell me the time, I'll pick you up at the airport. 2. I pick you up at the airport. 3. Therefore, you told me the time. #### Translating the Argument Let: - \( p \) represent "You tell me the time." - \( q \) represent "I pick you up at the airport." In symbolic form, the argument is: 1. \( p \to q \) 2. \( q \) 3. \(\therefore p \) #### Determining the Validity Next, we determine whether the argument is valid or invalid by comparing it with standard forms: - **Valid Argument Form:** - Modus Ponens: - \( p \to q \) - \( p \) - \(\therefore q \) - Modus Tollens: - \( p \to q \) - \( \neg q \) - \(\therefore \neg p \) - **Invalid Argument Form:** - Affirming the Consequent: - \( p \to q \) - \( q \) - \(\therefore p \) (This is the form presented here.) #### Conclusion Select the correct option below: - \( \ \text{A.} \) The argument is valid. In symbolic form the argument is \( p \to q, q, \therefore p \) - \( \ \text{B.} \) The argument is invalid. In symbolic form the argument is \( p \to q, q, \therefore p \) Choose option: \( \text{B} \) ### Explanation of the Diagram There isn't a diagram or graph associated with this problem. The question is focused solely on logical reasoning and symbolic representation.
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