Inductive vs Deductive Reasoning

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• Inductive vs Deductive Reasoning

Inductive vs Deductive Reasoning

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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.

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Deductive Reasoning

• Use 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.

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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.

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

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

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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.

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Law of Syllogism

• If 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.

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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.

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Law of Detachment or Law of Syllogism 1

• 1. If an angle is acute, then it is not obtuse.
• 2. ltABC is acute.
• 3. ltABC is not obtuse.
• Valid by Law of Detachment

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Law of Detachment or Law of Syllogism 2

• 1. Right angles are congruent.
• 2. ltA ltB
• 3. ltA and ltB are right angles.
• Invalid. Statement 1 is not a conditional
  statement.

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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.

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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.

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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.

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Law of Detachment or Law of Syllogism 6

• 1. If mlt240, then mlt3140
• 2. If mlt3140, then mlt440
• 3. If mlt240, then mlt440
• 4. Valid by Law of Syllogism

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

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Example 2

• If 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

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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

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Example 4

• If you cut class, then you will receive a
  detention. You cut class.
• Conclusion?
• You received a detention.
• Law of Detachment

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Example 5

• If Jay doesnt work hard, then he wont start the
  game and will quit the team. Jay quit the team.
• Conclusion?
• No conclusion. We do not why he quit the team.