
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
expand_more
expand_more
format_list_bulleted
Concept explainers
Question

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.
Expert Solution

This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution
Trending nowThis is a popular solution!
Step by stepSolved in 2 steps

Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.Similar questions
- Let p and q represent the following statements. p: The taxes are high. q: The job pays well. Write the compound statement -p + ~q in words. Choose the correct answer below. O A. The taxes are not high if and only if the job does not pay well. O B. The job pays well if and only if the taxes are not high. O C. If the taxes are high, then the job does not pay well. D. If the taxes are high, then the job pays well.arrow_forwardI don’t understand.arrow_forwardPlease type the answer. I'm having a problem figuring out what to put for the parenthesis and brackets for this.arrow_forward
- Determine whether the reasoning is an example of deductive or inductive reasoning. If the mechanic says that it will take seven days to repair your SUV, then it will actually take ten days. The mechanic says, "I figure it'll take exactly one week to fix it, ma'am." Then you can expect it to be ready ten days from now. Choose the correct answer below. A. The reasoning is deductive because general principles are being applied to specific examples. B. The reasoning is deductive because a general conclusion is being made from repeated observations of specific examples. C. The reasoning is inductive because a general conclusion is being made from repeated observations of specific examples. D. The reasoning is inductive because general principles are being applied to specific examples.arrow_forwardTranslate the sentence into symbolic form and define each letter you use. Being a chimpanzee is sufficient for not being a monkey. You get a refund or a store credit if the product is defective.arrow_forwardLet p represent the simple statement "The temperature is above 80°," q represent "We finished working," and r represent "We go to the pool." Write the symbolic statement q r ^ p in words. Choose the correct answer below. O A. If we have finished working or we go to the pool, then the temperature is above 80°. O B. We have finished working if and only if we go to the pool or the temperature is above 80°. O C. We have finished working if and only if we go to the pool and the temperature is above 80°. O D. If we have finished working, then we go to the pool and the temperature is above 80°.arrow_forward
- Determine whether the statement makes sense or does not make sense, and explain your reasoning. Saying "Ha!" is an exclamation and not a statement. Choose the correct answer below. O A. This makes sense. In logic, the concern is not solely with statements, and not all English sentences are statements. This does not make sense. In logic, the concern is solely with statements, and all English sentences are statements. This makes sense. An exclamation is not a statement because it is not either true or false. O B. O C. O D. This does not make sense. If a person says something to another person, then that person has made a statement.arrow_forwardDirection: Write the following in symbolic form (You may denote p, q or r). 4. Today is Monday if tomorrow is Tuesday. 5. Jun is a freshman and is taking photography.arrow_forwardHow do I translate it into symbolic form? If I do what I love, then I will be happy and if I don’t do what I love, then I won’t be happy.arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- Advanced Engineering MathematicsAdvanced MathISBN:9780470458365Author:Erwin KreyszigPublisher:Wiley, John & Sons, IncorporatedNumerical Methods for EngineersAdvanced MathISBN:9780073397924Author:Steven C. Chapra Dr., Raymond P. CanalePublisher:McGraw-Hill EducationIntroductory Mathematics for Engineering Applicat...Advanced MathISBN:9781118141809Author:Nathan KlingbeilPublisher:WILEY
- Mathematics For Machine TechnologyAdvanced MathISBN:9781337798310Author:Peterson, John.Publisher:Cengage Learning,

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

Numerical Methods for Engineers
Advanced Math
ISBN:9780073397924
Author:Steven C. Chapra Dr., Raymond P. Canale
Publisher:McGraw-Hill Education

Introductory Mathematics for Engineering Applicat...
Advanced Math
ISBN:9781118141809
Author:Nathan Klingbeil
Publisher:WILEY

Mathematics For Machine Technology
Advanced Math
ISBN:9781337798310
Author:Peterson, John.
Publisher:Cengage Learning,

