Which of the following best characterizes the following statements? A) if 1 <0 then 3 = 4 B) 1+1=3 if and only if 2 + 2 = 3 O Only A is true Only B is true O Both A and B are true O Both A and B are 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
icon
Related questions
icon
Concept explainers
Question
**Logical Reasoning Problem**

*Title: Evaluating Logical Statements: Practice Question*

**Question:**

Which of the following best characterizes the following statements?

**Statement A:** 
If 1 < 0 then 3 = 4

**Statement B:** 
1 + 1 = 3 if and only if 2 + 2 = 3

**Options:**

- Only A is true
- Only B is true
- Both A and B are true
- Both A and B are false

**Explanation of Concepts:**

- **Logical Implication (→):** A statement of the form "If P then Q" (P → Q) is considered true if P is false, regardless of the truth value of Q. It is also true if both P and Q are true. It is only false if P is true and Q is false.
  
- **Logical Biconditional (↔):** A statement of the form "P if and only if Q" (P ↔ Q) is true if both P and Q have the same truth values, either both are true or both are false.

**Detailed Explanation:**

1. **Evaluating Statement A:** 
   - Here, P: "1 < 0" which is false.
   - Q: "3 = 4" which is false.
   - P → Q: A false statement implies another false statement (False → False) is considered true by definition.

2. **Evaluating Statement B:**
   - First part: "1 + 1 = 3" which is false.
   - Second part: "2 + 2 = 3" which is also false.
   - P ↔ Q: Both parts of the statement are false, hence (False ↔ False) is true.

**Answer:**
- Both A and B are true.
Transcribed Image Text:**Logical Reasoning Problem** *Title: Evaluating Logical Statements: Practice Question* **Question:** Which of the following best characterizes the following statements? **Statement A:** If 1 < 0 then 3 = 4 **Statement B:** 1 + 1 = 3 if and only if 2 + 2 = 3 **Options:** - Only A is true - Only B is true - Both A and B are true - Both A and B are false **Explanation of Concepts:** - **Logical Implication (→):** A statement of the form "If P then Q" (P → Q) is considered true if P is false, regardless of the truth value of Q. It is also true if both P and Q are true. It is only false if P is true and Q is false. - **Logical Biconditional (↔):** A statement of the form "P if and only if Q" (P ↔ Q) is true if both P and Q have the same truth values, either both are true or both are false. **Detailed Explanation:** 1. **Evaluating Statement A:** - Here, P: "1 < 0" which is false. - Q: "3 = 4" which is false. - P → Q: A false statement implies another false statement (False → False) is considered true by definition. 2. **Evaluating Statement B:** - First part: "1 + 1 = 3" which is false. - Second part: "2 + 2 = 3" which is also false. - P ↔ Q: Both parts of the statement are false, hence (False ↔ False) is true. **Answer:** - Both A and B are true.
Expert Solution
steps

Step by step

Solved in 2 steps

Blurred answer
Knowledge Booster
Control Structure
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, computer-science and related others by exploring similar questions and additional content below.
Similar questions
Recommended textbooks for you
Database System Concepts
Database System Concepts
Computer Science
ISBN:
9780078022159
Author:
Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:
McGraw-Hill Education
Starting Out with Python (4th Edition)
Starting Out with Python (4th Edition)
Computer Science
ISBN:
9780134444321
Author:
Tony Gaddis
Publisher:
PEARSON
Digital Fundamentals (11th Edition)
Digital Fundamentals (11th Edition)
Computer Science
ISBN:
9780132737968
Author:
Thomas L. Floyd
Publisher:
PEARSON
C How to Program (8th Edition)
C How to Program (8th Edition)
Computer Science
ISBN:
9780133976892
Author:
Paul J. Deitel, Harvey Deitel
Publisher:
PEARSON
Database Systems: Design, Implementation, & Manag…
Database Systems: Design, Implementation, & Manag…
Computer Science
ISBN:
9781337627900
Author:
Carlos Coronel, Steven Morris
Publisher:
Cengage Learning
Programmable Logic Controllers
Programmable Logic Controllers
Computer Science
ISBN:
9780073373843
Author:
Frank D. Petruzella
Publisher:
McGraw-Hill Education