Questions and Answers
What is a conjecture?
What is a counterexample?
A specific case where a connective is false
Define deductive reasoning.
Use laws of logic to form a logical argument
What is the law of detachment?
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Explain the law of syllogism.
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What is inductive reasoning?
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Study Notes
Key Terms in Reasoning
- Conjecture: An unproven statement based on observations, often serving as a starting point for further investigation.
- Counterexample: A specific case that demonstrates the falsity of a conjectured statement or a connective, highlighting exceptions to general claims.
Types of Reasoning
- Deductive Reasoning: Involves constructing a logical argument using established laws of logic, deriving conclusions that are guaranteed if the premises are true.
- Inductive Reasoning: Involves identifying patterns from specific instances and then forming a general rule or conclusion based on those observations.
Logical Laws
- Law of Detachment: States that if the hypothesis of a true conditional statement is true, then the conclusion derived from that statement must also be true.
- Law of Syllogism: A principle that states if "If P then Q" and "If Q then R" are both true, it follows that "If P then R" is also true, allowing transitive deductions in logical arguments.
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Test your knowledge on inductive and reductive reasoning with these flashcards. Each card features key terms and their definitions that are essential for understanding logical reasoning. Perfect for students looking to enhance their critical thinking skills.
