Let p, q, and r represent simple statements as defined below. r: I am in debt. p: I have a job. q: I follow a budget. Write the following compound statement in symbolic form. Sufficient conditions for not being in debt are having a job and following a budget.
Let p, q, and r represent simple statements as defined below. r: I am in debt. p: I have a job. q: I follow a budget. Write the following compound statement in symbolic form. Sufficient conditions for not being in debt are having a job and following a budget.
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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![The image contains a logic exercise with symbolic representation of statements. Here's a detailed transcription suitable for an educational website:
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### Logic Exercise: Symbolic Representation of Statements
**Let p, q, and r represent simple statements as defined below:**
- **p:** I have a job.
- **q:** I follow a budget.
- **r:** I am in debt.
**Task:**
Write the following compound statement in symbolic form:
- "Sufficient conditions for not being in debt are having a job and following a budget."
**Solution Guide:**
To express the compound statement symbolically, note the sufficiency condition indicates a logical form:
- Not being in debt can be symbolized as "¬r."
- The condition "having a job and following a budget" is "p ∧ q."
Thus, the symbolic representation is:
- **(p ∧ q) → ¬r**
This means if you have a job and follow a budget, then you are not in debt.
**Exercise:**
Write the symbolic form of the statement below:
- __[Input Box: ( )]__
Fill in the symbolic representation following the logic used.
---
In this exercise, learners strengthen their understanding of symbolic logic used in conditional reasoning. They further apply this understanding to construct logical arguments.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe4cbdd14-a91f-4fea-8d0f-c81e5f41dd28%2F3b9b683f-5973-4da4-bbd4-0f7d0ca3de70%2Fckx775l_processed.png&w=3840&q=75)
Transcribed Image Text:The image contains a logic exercise with symbolic representation of statements. Here's a detailed transcription suitable for an educational website:
---
### Logic Exercise: Symbolic Representation of Statements
**Let p, q, and r represent simple statements as defined below:**
- **p:** I have a job.
- **q:** I follow a budget.
- **r:** I am in debt.
**Task:**
Write the following compound statement in symbolic form:
- "Sufficient conditions for not being in debt are having a job and following a budget."
**Solution Guide:**
To express the compound statement symbolically, note the sufficiency condition indicates a logical form:
- Not being in debt can be symbolized as "¬r."
- The condition "having a job and following a budget" is "p ∧ q."
Thus, the symbolic representation is:
- **(p ∧ q) → ¬r**
This means if you have a job and follow a budget, then you are not in debt.
**Exercise:**
Write the symbolic form of the statement below:
- __[Input Box: ( )]__
Fill in the symbolic representation following the logic used.
---
In this exercise, learners strengthen their understanding of symbolic logic used in conditional reasoning. They further apply this understanding to construct logical arguments.
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