pAT =T, where p is a proposition and T is tautology. True False
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
![**Logical Proposition Evaluation**
In the given expression:
\[ p \land T \equiv T \]
- **p** is a proposition.
- **T** is a tautology.
Select the appropriate answer:
- ☐ True
- ☐ False
**Explanation:**
This statement involves evaluating the logical conjunction of a proposition \( p \) with a tautology \( T \). In logic, a tautology is a statement that is always true. The conjunction operation \(\land\) results in true if and only if both operands are true. Here, for any proposition \( p\), the result of \( p \land T \) will be \( p \), not necessarily \( T \), since \( p \) could be false. Thus, the statement does not hold as a tautology and should be evaluated accordingly.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff4a5d476-fa3e-48a1-88f5-ec954230f216%2F95af41f5-06dd-4e9c-977d-f01c38f3cbf3%2Fs7u6bfo_processed.png&w=3840&q=75)
Transcribed Image Text:**Logical Proposition Evaluation**
In the given expression:
\[ p \land T \equiv T \]
- **p** is a proposition.
- **T** is a tautology.
Select the appropriate answer:
- ☐ True
- ☐ False
**Explanation:**
This statement involves evaluating the logical conjunction of a proposition \( p \) with a tautology \( T \). In logic, a tautology is a statement that is always true. The conjunction operation \(\land\) results in true if and only if both operands are true. Here, for any proposition \( p\), the result of \( p \land T \) will be \( p \), not necessarily \( T \), since \( p \) could be false. Thus, the statement does not hold as a tautology and should be evaluated accordingly.
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