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
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**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.
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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