Bell Work

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Bell Work
1. Discuss with your group the converse of the
statement. If it rains, then the car gets
wet and its truth value.. 2. Write the
statement above and its converse as a
biconditional. 3. Write the two conditional
statements that make up the biconditional.
Lines are skew if and only if they are
noncoplanar. Is each statement a good
definition? If not, find a counterexample. 4. Th
e midpoint of a line segment is the point that
divides the segment into two congruent segments.
5. A line segment is a part of a line.
If the car gets wet, then it rains.
Can not be done since converse is false.
If lines are skew, then they are noncoplanar if
lines are noncoplanar, then they are skew.
yes
No the statement is not reversible a ray.
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Bell Work

• PSAT booklets
• Page 13 (13-17)

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2.3 Deductive Reasoning

• Objectives
• Recognize and use Law of Detachment.
• Recognize and use Law of Syllogism.

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• Vocabulary
• Deductive Reasoning
• Law of Detachment
• Law of Syllogism

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Law of Detachment (pg 83)

• Side notes about this law
• You must be given a statement (p) about the
  hypothesis, not the conclusion.
• The Law of Detachment only uses one conditional.
• READ TOGETHER EXAMPLE PROBLEM 1 ON PAGE 82.

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In other words

• Law of detachment is used when a conditional and
  is true and you observe a statement or are told a
  statement about its hypothesis. Then you can
  conclude that the conclusion will occur.

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Example of Law of Detachment
A gardener knows that if it rains, the garden
will be watered. It is raining. It is raining
outside. What conclusion can he make?
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Law of Syllogism

• Side notes about this law
• It is similar to the transitive property you
  learned in Algebra (if ab and bc, then ac).
• It will take two conditional statements to use
  the law of syllogism.
• The conclusion of the one conditional must be the
  hypothesis of the other conditional (notice the
  qs above in the property box.

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In other words

• The law of syllogism combines two conditionals as
  one when the conclusion of the 1st conditionals
  is the hypothesis of the 2nd conditional.

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Examples of Law of Syllogism
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• Objectives
• Recognize and use Law of Detachment.
• Recognize and use Law of Syllogism.

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Bell Work (Day 2)
Use the three statements below. A. If games are
canceled, then Maria reads a book. B. If it
snows, then games are canceled. C. It is
snowing. 1. Using only statements A and B, what
can you conclude? 2. Using only statements B
and C, what can you conclude? 3. Using
statements A, B, and C, what can you
conclude? 4. Suppose both statement B and
games are canceled are true. Can you conclude
that statement C is true? Explain.
If it snows, then Maria reads a book.
Games are canceled.
Maria is reading a book.
No sample you cannot apply the Law of
Detachment.
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Homework

• Pgs 84-85 (1-33 odd)