Deductive Reasoning

1. Deductive Reasoning • Deductive reasoning is the process of making a logical argument by applying known facts, definitions, properties, and the laws of logic • If-then statements are typically used in deductive reasoning • If something is true then something else must be true • The “if” part of the statement is the hypothesis • The “then” part is the conclusion • Find the hypothesis and conclusion for each statement: • If the Red Sox defeat the Angels in the American League Divisional Series, then they will advance to the American League Championship Series • The teams that play in the World Series are the winners of the League Championship Series • If a team wins the LCS, then it will play in the World Series

2. 1 2 Laws of Logic • The laws of logic provide rules for determining whether statements used in deductive reasoning are true Law of Detachment • If the hypothesis of an if-then statement is true, then the conclusion is also true • Using the law of detachment • If a team wins four games in the ALCS, then it wins the ALCS • The Red Sox won four games in the 2004 ALCS • The Red Sox won the 2004 ALCS • Using the law of detachment in Geometry • If two angles are vertical angles, then the angles are congruent • 1 and 2 are vertical angles • 1 and 2 are congruent (or 1  2)

3. 2 1 2 Laws of Logic • The law of detachment only works in one direction • If two angles are vertical angles, then the angles are congruent • If two angles are congruent, then the angles are vertical angles • The Law of Syllogism is a rule that allows true statements to be linked together • If statement p then statement q • If statement q then statement r • If statement p then statement r • An example of a syllogism • If a team wins four games in the ALCS, then it wins the ALCS • If a team wins the ALCS, then it plays in the World Series • If a team wins four games in the ALCS, then it plays in the World Series If these two statements are true Then this statement is true