This worksheet will help you sharpen your logical reasoning skills by applying the Law of Detachment and exploring different types of syllogisms. Understanding these fundamental concepts is crucial for critical thinking and problem-solving in various aspects of life.
Section 1: The Law of Detachment
The Law of Detachment (also known as Modus Ponens) is a fundamental rule of inference in logic. It states:
If P, then Q. P. Therefore, Q.
Where 'P' represents a hypothesis and 'Q' represents a conclusion. If the hypothesis is true, then the conclusion must also be true.
Instructions: For each of the following, determine if the Law of Detachment applies. If it does, state the conclusion. If not, explain why.
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If it's raining, then the ground is wet. It's raining. Conclusion: _____________
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If a number is divisible by 4, then it's divisible by 2. The number 12 is divisible by 4. Conclusion: _____________
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If you study hard, you will pass the exam. You passed the exam. Conclusion: _____________ (Explain why or why not)
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If a triangle has three equal sides, then it is an equilateral triangle. Triangle ABC has three unequal sides. Conclusion: _____________ (Explain why or why not)
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If the sun is shining, then it is daytime. It is daytime. Conclusion: _____________ (Explain why or why not)
Section 2: Syllogisms
A syllogism is a type of logical argument that consists of three parts: a major premise, a minor premise, and a conclusion. The conclusion follows logically from the two premises. We'll focus on categorical syllogisms, which use categories to make inferences.
Instructions: Determine whether the following syllogisms are valid. If valid, state the conclusion. If invalid, explain why.
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Major Premise: All dogs are mammals. Minor Premise: Fido is a dog. Conclusion: _____________
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Major Premise: All squares are rectangles. Minor Premise: All rectangles are quadrilaterals. Conclusion: _____________
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Major Premise: Some birds are blue. Minor Premise: The robin is a bird. Conclusion: _____________ (Explain why or why not)
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Major Premise: No cats are dogs. Minor Premise: Mittens is a cat. Conclusion: _____________
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Major Premise: All fruits are sweet. Minor Premise: Tomatoes are fruits. Conclusion: _____________ (Explain why or why not – consider the accuracy of the major premise)
Section 3: Challenge Questions
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Create your own valid syllogism.
Major Premise: _____________ Minor Premise: _____________ Conclusion: _____________
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Create your own example using the Law of Detachment.
This worksheet provides a foundation for understanding the Law of Detachment and syllogisms. Practice with more examples to further strengthen your logical reasoning abilities. Remember to critically evaluate the premises of any argument before drawing a conclusion. By mastering these concepts, you’ll significantly improve your analytical and problem-solving skills.
