Deductive Reasoning

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TOPIC 2-3

• Deductive Reasoning

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TOPIC 2-3 Deductive Reasoning

• In 2-1, we learned that INDUCTIVE REASONING uses
• _________________ to reach a________________.
• This method of looking for a pattern does not
  always
• guarantee a true conjecture will be reached.
• A more accurate reasoning method is based on
  logic
• and is called _________________ _____________.
• Deductive reasoning uses __________ to make a
• ___________________. 66

conclusion
examples
deductive reasoning
rules
conclusion
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TOPIC 2-3 Deductive Reasoning

• Laws of Logic can help determine whether
• statements are true or false. If the patterns
• or rules of these laws are followed, a true
• conclusion is guaranteed.
• LAW OF DETACHMENT
• If is a true conditional and p is true,
• then q is true.
• Symbolically, you can look at it like this.
• 1)
• 2) p is true
• 3) q is true 66

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TOPIC 2-3 Deductive Reasoning

• For the 3 steps to work together to be true, the
• pattern must be followed exactly.
• EX 1 Can a true conclusion be reached using the
• Law of Detachment? If so, write the
  conclusion.
• 1) If two numbers are odd, then their sum is
  even.
• 2) 3 and 5 are odd.
• 3) ____________________________
• 67

p
q
(p is true)
the sum of 3 and 5 is even
(q is true)
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TOPIC 2-3 Deductive Reasoning

• EX 2 Can a true conclusion be reached using the
• Law of Detachment? If so, write the
  conclusion.
• 1) If I watch TV, I will not do my homework.
• 2) I did my homework.
• 3) __________________________________
  
• 67

q
p
(not q)
no conclusion
(the pattern was not followed exactly)
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TOPIC 2-3 Deductive Reasoning

• Examples 1 and 2 use the law of detachment to
  make
• a logical conclusion (when possible).
• Another Law of Logic is the Law of Syllogism.
• LAW OF Syllogism
• If and , then
• 1)
• 2)
• 3)
• 67

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TOPIC 2-3 Deductive Reasoning

• EX 3 Can a true conclusion be reached using the
  Law of Syllogism? If so, write the conclusion.
• 1) If Kari goes to the store, she will buy
  shampoo.
• 2) If Kari buys shampoo, she will wash her hair.
• 3) ________________________________.
• 68

If Kari goes to the store, she will wash her hair.
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TOPIC 2-3 Deductive Reasoning

• EX 4 Can a true conclusion be reached using the
  Law of Syllogism? If so, write the conclusion.
• 1) If you are a monkey, then you are a primate.
• 2) If you are a monkey, then you like bananas.
• 3) ________________________________.
• 68

No conclusion!
(pattern not followed exactly)
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TOPIC 2-3 Deductive Reasoning

• Determine if a valid conclusion can be reached
• from the two true statements. If so, write the
• conclusion and state which law is used.
• EX 5
• 1) If two angles are vertical, then two angles
  form a linear pair.
• 2) If two angles are vertical, then they are
  congruent.
• 3) ________________________________.
• 68

No conclusion!
(syllogism used incorrectly)
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TOPIC 2-3 Deductive Reasoning

• Determine if a valid conclusion can be reached
• from the two true statements. If so, write the
• conclusion and state which law is used.
• EX 6
• 1) If an angle is obtuse, then its measure is
  greater than 90 degrees.
• 2) Angle B is obtuse.
• 3) ________________________________.
• 69

(p is true)
Angle B has a measure greater than 90 degrees.
(q is true)
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TOPIC 2-3 Deductive Reasoning

• Determine if a valid conclusion can be reached
• from the two true statements. If so, write the
• conclusion and state which law is used.
• EX 7
• 1) If a number is an integer, then it is a
  rational number.
• 2) If a number is a rational number, it is a real
  number.
• 3) ________________________________. 69

If a number is an integer, then it is a real
number.
Law of Syllogism
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TOPIC 2-3 Deductive Reasoning

• Homework
• Pages 70 71