Get one of these

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Get one of these
Think about linear pairs degrees in a
triangle degrees in a quadrilateral
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Make a new notebook then do the problems below.
Warm up

• 2x 3 4 5x
• X -1/3
• 43 22 67 5x 2
• X 134/5
• v4
• 2, -2
• v9
• 3, -3
• v36
• 6, -6

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2.2 Intro to Logic

• Conditional Statements
• If-then form
• If a car is a Corvette, then it is a Chevrolet.
• Notation
• If p then q or p q
• Picking it apart
• If a car is a Corvette, then it is a Chevrolet.
• hypothesis conclusion
• (Notice if and then are not part of the
  hypothesis and conclusion.)

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Euler diagrams(pronounced Oiler)

• Often called Venn diagrams. Be sure you know
  both names.
• Our example If a car is a Corvette, then it is a
  Chevrolet.
• Since all Corvettes are Chevrolets, and Corvettes
  are just a piece of the Chevrolet line, here is
  what the Euler looks like
• (it would be safe to say that the hypothesis goes
  inside while the conclusion goes outside.)

Corvettes
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What about Susan?

• Consider this
• Susans car is a Corvette.
• Where does it belong in the diagram? (With
  Chevrolets or with Corvettes?)

• Corvettes
• Susans car

• The complete process of drawing a conclusion is
  called a logical argument.

• This 3 part argument is called a syllogism

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Our SYLLOGISM about Susan(3 parts)

• 1. If a car is a Corvette, then it is a
  Chevrolet.

2. Susans car is a Corvette.
3. Therefore, Susans car is a Chevrolet.
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Try this

• (Remember that an equilateral triangle is a
  triangle with 3 congruent sides.)
• (Remember that an isosceles triangle is a
  triangle with at least 2 congruent sides.)

Isoceles Triangles
Equilateral Triangles
? ABC
Draw an Euler diagram that conveys the following
information If a triangle is equilateral, then
the triangle is isosceles. ? ABC is equilateral.
What conclusion can you draw about ? ABC ?
? ABC IS ISOSCELES.
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CONVERSE

• A converse statement switches the hypothesis and
  conclusion of the conditional statement. (The
  if and then stay put)

Conditional If a car is a Corvette, then it is a
Chevrolet.
Converse If a car is a Chevrolet, then it is a
Corvette.
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Logical Chains

• Consider this
• If cats freak, then mice frisk.
• If sirens shriek, then dogs howl.
• If dogs howl, then cats freak.

We need to put these statements in a logical
order. So. The easiest way is to find a
conclusion that matches a hypothesis and make a
zig-zag pattern
If sirens shriek, then dogs howl. If dogs howl,
then cats freak. If cats freak, then mice frisk.
CONCLUSION If sirens shriek, then mice frisk.
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• The Logical Chain is also called
• Transitive Property.

If A then B, And if B then C Conclusion If A
then C.
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Quick Review

• What is another name for an if-then statement?
• What is the hypothesis part of an if-then
  statement?
• What is the conclusion part of an if-then
  statement?
• How do we make converse statement?
• What is an Euler diagram?
• Explain the Transitive property?
• How would you write this as a conditional
  statement All people who live in Ohio live in
  the United States.
• How would you write the previous statement as a
  converse statement?

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Assignment

• Pg 95, 9-33 all, ? 29