**Propositional Logic and Tautologies**In this lesson, we explore the concept of tautologies in propositional logic using truth tables. For this example, we have two propositions, $ p $ and $ q $, and we will analyze their combinations to determine if certain statements are tautologies.The following truth table for $ S1 $ and $ S2 $ is shown:| $ p $ | $ q $ | $ S1 $ | $ S2 $ ||:------:|:------:|:------:|:------:|| T | T | T | T || T | F | F | T || F | T | T | T || F | F | T | T |Based on the truth table above, we are to determine the tautology among the statements given.**Which statement is a tautology?**- $ O $ If not $ S1 $, then not $ S2 $.- $ O $ If $ S1 $, then $ S2 $.- $ O $ If $ S1 $, then not $ S2 $.- $ O $ If not $ S1 $, then $ S2 $.A tautology is a propositional formula that is always true regardless of the truth values of its subformulas.In this context, you are to analyze which of these statements always holds true based on the truth table values provided for $ S1 $ and $ S2 $.- Analyze each statement individually.- Verify its truth value for each combination of $ p $ and $ q $.**Diagrams:**The truth table provided above lists all possible combinations of the truth values of $ p $ and $ q $, along with their corresponding $ S1 $ and $ S2 $ values. This table is essential for determining which logical statements are tautologies.By methodically verifying each statement, you will deduce which one consistently holds true, thus identifying the tautology.

The truth table is :- p q s1 s2 T T F T F T T F T F T F F F T T

Answered: pre S1 and $2 are propositions in p and…

pre S1 and $2 are propositions in p and q. The truth table for S1 and 52 is shown as follows $1 $2 PTF+ Р OTTF Т Т F T T T F LLU F F F T T Which statement is a tautology?

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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Concept explainers

Bare bones programming language

Bare bones programming language is a low-level programming language that gives a detailed stepwise description of a program. It has a tight program design and in-depth understanding of the toolchain. It is based on the target environment and is used for safe coding practices. C programming language is a type of bare bones programming language.

Question

**Propositional Logic and Tautologies**

In this lesson, we explore the concept of tautologies in propositional logic using truth tables. For this example, we have two propositions, $ p $ and $ q $, and we will analyze their combinations to determine if certain statements are tautologies.

The following truth table for $ S1 $ and $ S2 $ is shown:

| $ p $ | $ q $ | $ S1 $ | $ S2 $ |
|:------:|:------:|:------:|:------:|
| T | T | T | T |
| T | F | F | T |
| F | T | T | T |
| F | F | T | T |

Based on the truth table above, we are to determine the tautology among the statements given.

**Which statement is a tautology?**

- $ O $ If not $ S1 $, then not $ S2 $.
- $ O $ If $ S1 $, then $ S2 $.
- $ O $ If $ S1 $, then not $ S2 $.
- $ O $ If not $ S1 $, then $ S2 $.

A tautology is a propositional formula that is always true regardless of the truth values of its subformulas.

In this context, you are to analyze which of these statements always holds true based on the truth table values provided for $ S1 $ and $ S2 $.

- Analyze each statement individually.
- Verify its truth value for each combination of $ p $ and $ q $.

**Diagrams:**

The truth table provided above lists all possible combinations of the truth values of $ p $ and $ q $, along with their corresponding $ S1 $ and $ S2 $ values. This table is essential for determining which logical statements are tautologies.

By methodically verifying each statement, you will deduce which one consistently holds true, thus identifying the tautology.

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