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Get one of these. Think about *linear pairs *degrees in a triangle *degrees in a quadrilateral. Make a new notebook, please. Intro to Logic 2.1 and 2.2. Conditional Statements If-then form: If a car is a Corvette, then it is a Chevrolet. Notation: If p then q or p q

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get one of these
Get one of these

Think about

*linear pairs

*degrees in a triangle

*degrees in a quadrilateral

intro to logic 2 1 and 2 2

Intro to Logic 2.1 and 2.2

Conditional Statements

If-then form:

Ifa car is a Corvette, thenit is a Chevrolet.

Notation:

Ifp thenq or pq

Picking it apart:

Ifa car is a Corvette,thenit is a Chevrolet.

hypothesis conclusion

(Notice “if” and “then” are not part of the hypothesis and conclusion.)

euler diagrams pronounced oiler
Euler diagrams(pronounced “Oiler”)

Chevrolets

  • 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

Chevrolets

what about susan
What about Susan?
  • Consider this:
    • Susan’s car is a Corvette.
    • Where does it belong in the diagram? (With Chevrolets or with Corvettes?)

Chevrolets

  • The complete process of drawing a conclusion is called a logical argument.
  • Corvettes
  • Susan’s Car
  • This 3 part argument is called a syllogism
our syllogism about susan 3 parts
Our SYLLOGISM about Susan(3 parts)

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

2. Susan’s car is a Corvette.

3. Therefore, Susan’s car is a Chevrolet.

try this

But first, tap into your prior knowledge

Try this:

Isosceles Triangles

  • An equilateral triangle has 3 congruent sides.
  • An isosceles triangle has at least 2 congruent sides.

Equilateral

Triangles

Draw an Euler diagram that conveys the following information:

If a triangle is equilateral, then the triangle is isosceles.

∆ ABC is equilateral.

∆ ABC

What conclusion can you draw about ∆ ABC ?

∆ ABC IS ISOSCELES.

quick review
Quick Review
  • What is another name for an if-then statement?
  • What is the hypothesis part of “If it’s my dog, then he has fleas”?
  • What is the conclusion part of “If it’s Monday, then we’re having meatloaf”?
  • It’s Monday. What can you conclude?
  • It’s Tuesday. What can you conclude? (be careful)
  • What is an Euler diagram?
  • How would you write this as a conditional statement: All people who live in Ohio live in the United States.
  • What is a three part argument called?
converse
CONVERSE

A converse statement switches the hypothesis and conclusion of the conditional statement. (The ‘if’ and ‘then’ stay put) q p

Conditional:

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

Converse:

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

inverse statement
Inverse Statement

Negate the hypothesis and conclusion of the conditional statement.

Conditional:

If it’s hot outside, then the sun is shining.

Inverse:

If it’s not hot outside, then the sun is not shining.

related conditional statements conditional p q converse q p inverse p q contrapositive q p
Related Conditional Statements

Conditional p q

Converse q p

Inverse ~p ~q

Contrapositive ~q ~p

contrapositive statement
Contrapositive Statement

SWITCH the hypothesis and conclusion of the INVERSE statement.

Conditional:

If it’s hot outside, then the sun is shining.

Inverse:

If it’s not hot outside, then the sun is not shining.

Contrapositive:

If the sun is not shining, then it is not hot outside.

slide13

Counterexample – an example used to show something is false.

Example: If it’s my dog, then it has fleas.

Counterexample: It could be your dog.

slide14
$ $ $ $ $ $ $
  • Using the sentence: “My dog has fleas”, write the (a) conditional, (b) converse, (c) inverse and (d) contrapositivestatements.

A) If it is my dog, then it has fleas

B) If it has fleas, then it is my dog.

C) If it is not my dog, then it does not have fleas.

D) If it does not have fleas, then it is not my dog.

One more time… Use the sentence “Blazers are awesome.”

slide15

Assignment

  • 2.1 and 2.2 Practice Worksheets
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