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2.3 Deductive Reasoning

This guide explores deductive reasoning as a systematic method of deriving conclusions using logical order. Learn to represent logical statements through symbolic notation, such as the implication symbol (→), negation (~), and bi-conditional (↔). Understand key concepts such as conditional statements, converses, inverses, and contrapositives through examples, like the Law of Detachment and the Law of Syllogism. This fundamental approach differentiates deductive reasoning from inductive reasoning, providing a solid foundation for constructing logical arguments.

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2.3 Deductive Reasoning

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  1. 2.3 Deductive Reasoning Deductive means “a systematic method of deriving conclusions”

  2. 2-3 Deductive Reasoning • You will use symbolic notation to represent logical statements. • You will learn to form conclusions by applying the laws of logic to the statements

  3. Symbolic Notation prepresents the hypothesis qrepresents the conclusion → is read as “implies” ~ represents negation If p then q can be written as p →q Inverse statement ~p → ~q Bi-conditional statement p ↔ q

  4. How would you represent each of the following “symbolically?” Conditional Converse Inverse Contrapositive

  5. Deductive Reasoning • Deductive reasoning uses facts, definitions, and accepted properties in a logical order to write a logical argument. • Inductive reasoning uses previous examples and patterns to make a conjecture.

  6. Laws of Deductive Reasoning • Law of Detachment: If p →q is a true conditional statement and p is true, that is, the situation described in the hypothesis occurs, then q is true, that is, the conditional situation also occurs. If it snows 10 feet, then there is no school. It just snowed 10 feet, so I can conclude there is no school.

  7. Laws of Deductive Reasoning • Law of Syllogism: If p →q and q →r are true conditional statement, then p →r is true p: John gets a C q: John passes the test r: John plays football If John gets a C, then john plays football.

  8. Write the Converse, Inverse, and Contrapositive in symbolic notation. • C. Statement: If it is Wednesday, then I am not home. • Converse: If I am not at home, then it is Wednesday. • Inverse: If it is not Wednesday, then I am home. • Contrapositive: If I am home, then it is not Wednesday.

  9. Write the Converse, Inverse, and Contrapositive (include symbolic notation). • If 3 measures 90, then 3 is not acute. • If 3 is not acute, then 3 measures 90. • If 3 does not measure 90, then 3 is acute. • If 3 is acute, then 3 does not measure 90.

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