inductive vs deductive reasoning

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Inductive vs Deductive Reasoning Inductive vs Deductive Reasoning

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Inductive vs Deductive Reasoning. Inductive vs Deductive Reasoning. Inductive Reasoning. When we make conjectures based on observations. Ex. For 3 weeks, the cafeteria served pizza on Wednesday. I conclude next Wed. the cafeteria will have pizza. Deductive Reasoning. - PowerPoint PPT Presentation

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Page 1: Inductive vs Deductive Reasoning

Inductive vs Deductive Reasoning

Inductive vs Deductive Reasoning

Page 2: Inductive vs Deductive Reasoning

Inductive Reasoning

When we make conjectures based on observations.

Ex. For 3 weeks, the cafeteria served pizza on Wednesday. I conclude next Wed. the cafeteria will have pizza.

Page 3: Inductive vs Deductive Reasoning

Deductive ReasoningUse facts, definitions and accepted

properties in logical order to write a logical argument.

Ex. Dictionaries are useful books. Useful books are valuable. Therefore, dictionaries are valuable.

Page 4: Inductive vs Deductive Reasoning

Inductive or Deductive??

1. Julie knows that Dell computers cost less than Gateway computers. Julie also knows that Gateway computers cost less than compaq computers. Julie reasons that Dell computers cost less than compaq computers.

Deductive Reasoning.

Page 5: Inductive vs Deductive Reasoning

2. If you live in Nevada and are between ages of 16 and 18, then you must take driver’s education classes to get your license. Mark has always lived in Nevada, is 16, and has his driver’s license. Therefore, Mark took driver’s education classes.

Deductive Reasoning

Page 6: Inductive vs Deductive Reasoning

3. Matt noticed that every Tuesday since school started it has rained. Matt thinks it is going to rain next Tuesday.

Inductive reasoning.

Page 7: Inductive vs Deductive Reasoning

Law of Detachment

If p q is a true conditional statement and p is true, then q is true.

Ex. If I pass the test, then I get an A in geometry. I passed the test. So I got an A in geometry.

Page 8: Inductive vs Deductive Reasoning

Law of SyllogismIf p q and q r are true conditional

statements, then p r is true.Ex. If I pass the test, then I get an A

in geometry. If I get an A in geometry, then I get a new car.

Conclusion. I passed the test so I get a new car.

Page 9: Inductive vs Deductive Reasoning

Example 6

Determine if statement (3) follows from statement (1) and (2) by the Law of Detachment or the Law of Syllogism. If it does, state which law was used. If it does not, write invalid.

Page 10: Inductive vs Deductive Reasoning

Law of Detachment or Law of Syllogism #1

1. If an angle is acute, then it is not obtuse.

2. <ABC is acute.3. <ABC is not obtuse.Valid by Law of Detachment

Page 11: Inductive vs Deductive Reasoning

Law of Detachment or Law of Syllogism #2

1. Right angles are congruent.2. <A <B3. <A and <B are right angles.Invalid. Statement 1 is not a

conditional statement.

Page 12: Inductive vs Deductive Reasoning

Law of Detachment or Law of Syllogism #3

1. If you save a penny, then you have earned a penny.

2. Art saves a penny.3. Art has earned a penny. Valid by Law of Detachment.

Page 13: Inductive vs Deductive Reasoning

Law of Detachment or Law of Syllogism #4

1. If you are a teenager, then you are always right.

2. If you are always right, then people will listen to you.

3. If you are a teenager, then people will listen to you.

Valid by Law of Syllogism.

Page 14: Inductive vs Deductive Reasoning

Law of Detachment or Law of Syllogism #5

1. If you drive 50 miles per hour in a school zone, then you will get a speeding ticket.

2. Pat received a speeding ticket.3. Pat was driving 50 miles per hour

in a school zone. Invalid. Pat could have received a

speeding ticket for speeding on the highway.

Page 15: Inductive vs Deductive Reasoning

Law of Detachment or Law of Syllogism #6

1. If m<2=40°, then m<3=140°2. If m<3=140°, then m<4=40°3. If m<2=40°, then m<4=40°4. Valid by Law of Syllogism

Page 16: Inductive vs Deductive Reasoning

Write a conclusion using the true statements. If no conclusion is possible, write no conclusion.

Page 17: Inductive vs Deductive Reasoning

Example 1

If Tim gets stung by a bee, then he will get very ill. If he gets very ill, then he will go to the hospital. Tim gets stung by a bee.

Conclusion?Tim will go to the hospital.Law of Syllogism

Page 18: Inductive vs Deductive Reasoning

Example 2If Hank applies for the job, then he will

be the new lifeguard at the pool. If he is the new lifeguard at the pool, then he will buy a new car. Hank applies for the job.

Conclusion?Hank will buy a new car.Law of Syllogism

Page 19: Inductive vs Deductive Reasoning

Example 3

If two planes intersect, then their intersection is a line. Plane A and plane B intersect.

Conclusion?Plane A and plane B intersect

in a line.Law of Detachment

Page 20: Inductive vs Deductive Reasoning

Example 4

If you cut class, then you will receive a detention. You cut class.

Conclusion?You received a detention.Law of Detachment

Page 21: Inductive vs Deductive Reasoning

Example 5

If Jay doesn’t work hard, then he won’t start the game and will quit the team. Jay quit the team.

Conclusion?No conclusion. We do not why

he quit the team.