Questions and Answers
What is the Law of Detachment?
A law of logic in which two original statements may lead to a concluding statement. 'If P, then Q. It is given that P is true.' -> Q is true.
What is the Law of Syllogism?
A law of logic in which two original statements may lead to a concluding statement. 'If P, then Q. If Q, then R.' -> If P, then R follows.
Can a conclusion be drawn from the statements 'All dogs bark. Milo barks.'?
No conclusion can be drawn (Law of Detachment cannot be applied).
What conclusion can be drawn from 'All mammals have fur. A serval is a mammal.'?
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What conclusion can be drawn from 'If Mark doesn't wear safety glasses, he'll get a speck in his eye. If Mark gets a speck in his eye, he'll go to the doctor.'?
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Apply the Law of Detachment to the statement 'All teachers love math. Mr. Chamberlain loves math.' Can a conclusion be drawn?
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What conclusion can be drawn from 'If Marty gets his license, he will buy a car. If Marty buys a car, he will get a Mustang.'?
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Study Notes
Laws of Logic: Detachment and Syllogism
- Law of Detachment: If "If P, then Q" is true, and P is true, then Q must be true.
- Example: Given "If Mark doesn't wear safety glasses, he'll get a speck in his eye" and "If Mark gets a speck in his eye, he'll go to the doctor," leads to the conclusion that if Mark doesn't wear safety glasses, he will go to the doctor.
Application of the Laws
- Law of Syllogism: If "If P, then Q" and "If Q, then R" are both true, then "If P, then R" is also true.
- Example: From "If Marty gets his license, he will buy a car" and "If Marty buys a car, he will get a Mustang," concludes that if Marty gets his license, he will get a Mustang.
Application Scenarios
- Scenario without Conclusion: Consider all dogs bark, and Milo barks. No conclusion can be drawn since it doesn't confirm if Milo is a dog or not; Law of Detachment cannot be applied.
- Valid Conclusion Example: From the statements "All mammals have fur" and "A serval is a mammal," it can be concluded that a serval has fur.
Limitations of the Laws
- Not all statements lead to conclusive outcomes when applying the laws.
- Recognizing when a conclusion cannot be drawn is essential for logical reasoning and application of logical laws.
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Description
Test your understanding of the Laws of Syllogism and Detachment with this quiz. These fundamental laws of logic are essential for drawing conclusions from given statements. Challenge yourself with definitions and applications of these concepts.
