(~p V q) ^ (~p → q) 25. р
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
Related questions
Question
Construct a truth table using T and F to determine whether the argument is valid or invalid.
T: True
F: False
![The given image contains a logical expression problem and a numbered statement. The expression is:
\[
(\sim p \lor q) \land (\sim p \to q)
\]
The numbered statement is:
\[
25. \quad \frac{p}{\sim q}
\]
**Explanation:**
1. **Logical Expression:**
- \((\sim p \lor q)\) is a disjunction, meaning "not p or q."
- \((\sim p \to q)\) is an implication, meaning "if not p, then q."
- The conjunction \(\land\) combines these two statements, indicating that both must be true.
2. **Numbered Statement (25):**
- This represents a logical deduction problem.
- \(\frac{p}{\sim q}\) implies that from the premise \(p\), one should deduce \(\sim q\).
This setup is typical in logical reasoning exercises aimed at practicing deduction using logical operators.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F119977c1-3a9f-4ed7-9f2b-cc635011c7d9%2Fe6005d33-7a8e-47c5-91f1-8eefd22bc9fa%2Fr3090ef_processed.png&w=3840&q=75)
Transcribed Image Text:The given image contains a logical expression problem and a numbered statement. The expression is:
\[
(\sim p \lor q) \land (\sim p \to q)
\]
The numbered statement is:
\[
25. \quad \frac{p}{\sim q}
\]
**Explanation:**
1. **Logical Expression:**
- \((\sim p \lor q)\) is a disjunction, meaning "not p or q."
- \((\sim p \to q)\) is an implication, meaning "if not p, then q."
- The conjunction \(\land\) combines these two statements, indicating that both must be true.
2. **Numbered Statement (25):**
- This represents a logical deduction problem.
- \(\frac{p}{\sim q}\) implies that from the premise \(p\), one should deduce \(\sim q\).
This setup is typical in logical reasoning exercises aimed at practicing deduction using logical operators.
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