133 Converse, Inverse, and Contrapositive

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13-3 Converse, Inverse, and Contrapositive
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Read Explore top pg 500
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Definition

• Negation---saying the opposite of what was being
  said previously
• This can be done by adding not to the
  statement or by saying It is not the case that

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Example 1

• Statement
• The dog is big
• Negation
• The dog is not big
• or
• It is not the case that the dog is big

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Notation

• The symbol we use for negation is
• We can use a letter to represent a statement
• Ex p The dog is big
• What is p ????

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Example 2

• Write the negation of the statement in two ways
• p The football has laces
• p
• or
• p

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Notation

• Hypothesis statement containing the word if
• Ex. P If the instrument is a guitar
• Conclusion Statement containing the word then
• Ex. Q Then the instrument has strings
• When putting these together we get p q
• Where refers to an if-then relationship

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Example 3

• Statement If p then q p q
• Converse If q then p q p
• Inverse If p then q p q
• Contrapositive If q then p q p

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Example 4

• Refer to boxes on the top of pg 501

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Example 5

• Write the inverse of the statement and tell if it
  is true or false.
• Statement If two angles are right angles, then
  the angles are congruent p q
• Inverse p q
• Write the inverse and then determine if it is
  true or false

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Counterexample

• Two angles having a measure of 45 degrees are
  congruent but are not right angles.

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Example 6

• Write the contrapositive of the statement and
  tell whether or not it is true or false
• Statement p q If a figure is a rectangle,
  then the figure is a polygon
• Contrapositive q p
• True or False

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Example 7

• Write the converse of the statement and tell
  whether it is true or false
• Statement If a figure is a rectangle, then it
  is a square. True or False
• Converse
• True or false

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Classwork

• Pg 502 1-4, 10-16 even