Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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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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