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Questions and Answers
What does entailment refer to?
What does entailment refer to?
- A relationship between two contradictory statements
- A logical relationship between two statements where the truth of one guarantees the truth of another (correct)
- A statement that is always false
- A relationship between a statement and its negation
Which of the following best describes a contradiction?
Which of the following best describes a contradiction?
- A statement that is always true
- The relationship between two statements that cannot both be true (correct)
- The relationship between two statements that can both be true
- A statement that is neither true nor false
If statement A entails statement B, what does this mean?
If statement A entails statement B, what does this mean?
- If A is true, then B must also be false
- If A is false, then B must be true
- If B is true, then A must also be true
- If A is true, then B must also be true (correct)
In a complex statement containing contradictory statements A and B, what is the resulting complex statement called?
In a complex statement containing contradictory statements A and B, what is the resulting complex statement called?
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Why can a contradiction never be true?
Why can a contradiction never be true?
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Study Notes
Entailment
- Entailment refers to a logical relationship where if statement A is true, then statement B must also be true. This means that A guarantees the truth of B.
Contradiction
- A contradiction occurs when two statements cannot both be true at the same time. It is typically characterized by a direct opposition in truth values between the statements.
Meaning of A entails B
- When it is stated that A entails B, it implies that the truth of A is sufficient to establish the truth of B. If A occurs, B will necessarily follow.
Resulting Complex Statement with Contradictions
- In a complex statement containing contradictory statements A and B, the resulting statement is termed a "contradiction." This is distinguished by the inherent conflict between A and B, rendering them mutually exclusive.
Truth of a Contradiction
- A contradiction can never be true because it violates the fundamental principle of logic that states that contradictory statements cannot coexist in the same context. If one statement is true, the other must be false.
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Description
Explore the concept of entailment in logic, where the truth of one statement guarantees the truth of another. Learn how to determine if one statement entails another and the implications of this logical relationship.
