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Using deductive reasoning.

Objective. Using deductive reasoning. Vocabulary. deductive reasoning. Deductive reasoning is the process of using logic to draw conclusions from given facts, definitions, and properties. Example 1A: Media Application. Is the conclusion a result of inductive or deductive reasoning?.

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Using deductive reasoning.

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  1. Objective Using deductive reasoning.

  2. Vocabulary deductive reasoning

  3. Deductive reasoning is the process of using logic to draw conclusions from given facts, definitions, and properties.

  4. Example 1A: Media Application Is the conclusion a result of inductive or deductive reasoning? There is a myth that you can balance an egg on its end only on the spring equinox. A person was able to balance an egg on July 8, September 21, and December 19. Therefore this myth is false. Since the conclusion is based on a pattern of observations, it is a result of inductive reasoning.

  5. Example 1B: Media Application Is the conclusion a result of inductive or deductive reasoning? There is a myth that the Great Wall of China is the only man-made object visible from the Moon. The Great Wall is barely visible in photographs taken from 180 miles above Earth. The Moon is about 237,000 miles from Earth. Therefore, the myth cannot be true. The conclusion is based on logical reasoning from scientific research. It is a result of deductive reasoning.

  6. Check It Out! Example 1 There is a myth that an eelskin wallet will demagnetize credit cards because the skin of the electric eels used to make the wallet holds an electric charge. However, eelskin products are not made from electric eels. Therefore, the myth cannot be true. Is this conclusion a result of inductive or deductive reasoning? The conclusion is based on logical reasoning from scientific research. It is a result of deductive reasoning.

  7. Another valid form of deductive reasoning is the Transitive Property (or Law of Syllogism). It allows you to draw conclusions from two conditional statements when the conclusion of one is the hypothesis of the other. Law of Syllogism (Transitive relation) If p q and q  r are true statements, then p  r is a true statement.

  8. Properties of Equality and Real Numbers Addition Property: Subtraction Property: Multiplication Property: Division Property: Substitution Property: Distributive Property:

  9. Properties of Congruence Reflexive Property: Symmetric Property: Transitive Property:

  10. Lesson Quiz: Part II Determine if each conjecture is valid? 2. Given: If n is a natural number, then n is an integer. If n is an integer, then n is a rational number. 0.875 is a rational number. Conjecture: 0.875 is a natural number. not valid 3. Given: If an American citizen is at least 18 years old, then he or she is eligible to vote. Anna is a 20-year-old American citizen. Conjecture: Anna is eligible to vote. valid

  11. Homework: Page-50 Problems 1-10

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