Construct a truth table using T and F to determine whether the argument is valid or invalid. T: TrueF: 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.

Answered: Image /qna-images/answer/e6005d33-7a8e-47c5-91f1-8eefd22bc9fa.jpg

Answered: (~p V q) ^ (~p → q) 25. р

Engineering

Computer Science

(~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

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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.

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