Symbolize the statement: Gail will take a Latin class or a psychology class if and only if she is a history major. with the simple statements p -- Gail is a history major q-- Gail takes a Latin class T-- Gail takes a psychology class Use the toolbar that pops up when you click the answer box to enter logic symbols. The computer uses the symbol instead of and instead of . Check Answer
Symbolize the statement: Gail will take a Latin class or a psychology class if and only if she is a history major. with the simple statements p -- Gail is a history major q-- Gail takes a Latin class T-- Gail takes a psychology class Use the toolbar that pops up when you click the answer box to enter logic symbols. The computer uses the symbol instead of and instead of . Check Answer
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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![## Symbolizing Logical Statements
### Problem Statement
Symbolize the following statement:
"**Gail will take a Latin class or a psychology class if and only if she is a history major.**"
### Given Simple Statements
- **p**: Gail is a history major
- **q**: Gail takes a Latin class
- **r**: Gail takes a psychology class
### Instructions
Use the toolbar that appears when you click the answer box to enter logical symbols. The computer uses the following symbols:
- **→** instead of →
- **⇔** instead of ↔
### Solution
To symbolize the given statement using the provided simple statements, we recognize that we need to use logical equivalence (↔) for the phrase "if and only if." Our statement involves both **q** (Latin class) and **r** (psychology class) combined with an OR operation.
The symbolic form would be:
\[
(q \lor r) \leftrightarrow p
\]
This represents:
_(Gail will take a Latin class or a psychology class) if and only if she is a history major_.
**Graphical Explanation**:
The relationship between the variables **p**, **q**, and **r** is charted using logical symbols:
1. **q ∨ r** implies that either **q** (Latin class) or **r** (psychology class) can occur.
2. **q ∨ r ⇔ p** signifies that the occurrence of either **q** or **r** is logically equivalent to **p** (Gail being a history major).
### Check Solution
The interface provides a textbox for input and a "Check Answer" button to validate if the entered symbolic relationship is correct. Ensure the correct logical syntax is used as per the instructions.
---
This symbolization exercise is an essential part of understanding how to convert natural language statements into formal logic, which is crucial in fields like mathematics, computer science, and philosophy.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa6fffe07-0182-49b4-949f-7de773e92073%2F334f777f-3a32-4ced-baa5-74a08046ab69%2F6yxutoo_processed.jpeg&w=3840&q=75)
Transcribed Image Text:## Symbolizing Logical Statements
### Problem Statement
Symbolize the following statement:
"**Gail will take a Latin class or a psychology class if and only if she is a history major.**"
### Given Simple Statements
- **p**: Gail is a history major
- **q**: Gail takes a Latin class
- **r**: Gail takes a psychology class
### Instructions
Use the toolbar that appears when you click the answer box to enter logical symbols. The computer uses the following symbols:
- **→** instead of →
- **⇔** instead of ↔
### Solution
To symbolize the given statement using the provided simple statements, we recognize that we need to use logical equivalence (↔) for the phrase "if and only if." Our statement involves both **q** (Latin class) and **r** (psychology class) combined with an OR operation.
The symbolic form would be:
\[
(q \lor r) \leftrightarrow p
\]
This represents:
_(Gail will take a Latin class or a psychology class) if and only if she is a history major_.
**Graphical Explanation**:
The relationship between the variables **p**, **q**, and **r** is charted using logical symbols:
1. **q ∨ r** implies that either **q** (Latin class) or **r** (psychology class) can occur.
2. **q ∨ r ⇔ p** signifies that the occurrence of either **q** or **r** is logically equivalent to **p** (Gail being a history major).
### Check Solution
The interface provides a textbox for input and a "Check Answer" button to validate if the entered symbolic relationship is correct. Ensure the correct logical syntax is used as per the instructions.
---
This symbolization exercise is an essential part of understanding how to convert natural language statements into formal logic, which is crucial in fields like mathematics, computer science, and philosophy.
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