### Translating Arguments into Symbolic FormThis 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 Argument1. 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 ArgumentLet:- $ 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 ValidityNext, 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.)#### ConclusionSelect 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 DiagramThere isn't a diagram or graph associated with this problem. The question is focused solely on logical reasoning and symbolic representation.

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

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Concept explainers

Logic and Proofs

Discrete mathematics deals with the separated values of data such as integers. It is widely used in the practical field of computer science and mathematics. By knowing discrete mathematics one can improve their reasoning and problem-solving capabilities. Discrete mathematics became popular after the boom of computers which operate in discrete steps and store data in discrete bits. It also useful in studying computer programming, algorithms, and cryptography.

Question

### 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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