Vocabulary Review: Deductive Reasoning, Law of Detachment, and Law of Syllogism

Deductive Reasoning

• Definition: The process of drawing a conclusion based on predetermined facts, properties, or definitions.
  • Involves knowing specific laws, definitions, or properties to make a conclusion.
  • Example: Understanding a certain law allows you to draw conclusions based on it.

Law of Detachment

• Notation: If P then Q (conditional statement)
  • Hypothesis (P) and Conclusion (Q)
• Concept:
  • If a conditional statement is true, then both the hypothesis and conclusion must also be true.
  • Example:
    • Statement: "If I finish my chores, then I can go to the movies with my friends."
    • Interpretation: If it’s true that finishing chores allows one to go to the movies, then if the chores are completed, going to the movies is consequently true.

Law of Syllogism

• Notation:
  • If P then Q
  • If Q then R
• Concept:
  • If both conditional statements are true, then a new conditional statement "If P then R" is also true.
  • This involves using the conclusion of the first statement as the hypothesis for the second.
  • Example:
    • Statements:
      • "If an animal is a bear, then it is a wild animal."
      • "If an animal is wild, then it is dangerous."
    • Conclusion: Therefore, "If an animal is a bear, then it is dangerous."

Both concepts apply when the initial conditions and connections between them are true, allowing one to infer new conclusions from established premises.