2 4 Deductive Reasoning OBJECTIVES Use the Law

2. 4 Deductive Reasoning

OBJECTIVES: • Use the Law of Detachment and Law of Syllogism. 2. 4 Deductive Reasoning

VOCABULARY: • • Deductive Reasoning Inductive Reasoning Law of Detachment Law of Syllogism 2. 4 Deductive Reasoning

SOLVE IT! 2. 4 Deductive Reasoning

Deductive vs. Inductive Reasoning • The difference: inductive reasoning uses patterns to arrive at a conclusion (conjecture) deductive reasoning uses facts, rules, definitions or properties to arrive at a conclusion. 2. 4 Deductive Reasoning

Deductive reasoning is the process of reasoning logically from given statements to a conclusion. 2. 4 Deductive Reasoning

Examples of Inductive Reasoning 1) Every quiz has been easy. Therefore, the test will be easy. 2) The teacher used Power. Point in the last few classes. Therefore, the teacher will use Power. Point tomorrow. 3) Every fall there have been hurricanes in the tropics. Therefore, there will be hurricanes in the tropics this coming fall. 2. 4 Deductive Reasoning

Example of Deductive Reasoning An Example: The catalog states that all entering freshmen must take a mathematics placement test. You are an entering freshman. Conclusion: You will have to take a mathematics placement test. 2. 4 Deductive Reasoning

Inductive or Deductive Reasoning? Geometry example… x Triangle sum property – the sum of the angles of any triangle is always 180 degrees. Therefore, angle x = 30° 60◦ Deductive Reasoning – conclusion is based on a property 2. 4 Deductive Reasoning

Inductive or Deductive Reasoning? Geometry example… What comes next? Is there a rule? Colored triangle rotating 90° CW in the corners of the square Inductive Reasoning 2. 4 Deductive Reasoning

2. 4 Deductive Reasoning

2. 4 Deductive Reasoning

Deductive Reasoning Is… • Deductive reasoning is when you start from things you assume to be true, and draw conclusions that must be true if your assumptions are true. For Example All dogs have a tail. Buddy is a dog. Therefore Buddy has a tail. 2. 4 Deductive Reasoning

How Can Deductive Reasoning Be Applied In School? Math Scott has a case of soda in his house since there are 13 cans of soda left I deduce that Scott has drank 11 cans of soda. English When I see ‘like’ in a sentence, I deduce that it is a simile. 2. 4 Deductive Reasoning

Science Using laws and rules to make assumptions The law of gravity means everything that goes up must come down I threw a baseball in the air That means the baseball must come down. Social Studies To be elected President you must obtain at least 270 electoral votes George Bush won 287 electoral votes Therefore George Bush is the President. 2. 4 Deductive Reasoning

2. 4 Deductive Reasoning

Law of Detachment: You can use this law to provide conclusions to statements. 2. 4 Deductive Reasoning

If M is the midpoint of a segment, then it divides the segment into two congruent segments. Given: M is the midpoint of You can conclude that M divides . into two congruent segments, or 2. 4 Deductive Reasoning

If an angle is obtuse, then it is not acute. is not obtuse. The converse of the assumption is not true, so It is not possible to conclude that is acute. 2. 4 Deductive Reasoning

Law of Syllogism: You can use this law to state a conclusion from two true conditional statement. 2. 4 Deductive Reasoning

If a figures is a square, then the figure is a rectangle. If a figure is a rectangle, then the figure has four sides. Conclusion: if the figure is a square, then the figure has four side. If you practice your math, then you will get good grades. If you get good grades in math, then you will pass the class. Conclusion: if you practice your math, then you will pass the class. 2. 4 Deductive Reasoning

Lesson Check: 2. 4 Deductive Reasoning

Lesson Check: 2. 4 Deductive Reasoning