Warm up

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Warm up!!!

• Evaluate for the given value of x
• 1) 9x 13 x 7
• 2) 90 3x x 31
• Solve Each Equation
• 3) 2( x 4 ) x 13
• 4) 2(3x 4) 10 5 (x 4)
• 5) 14x 2( 5x 14)

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Section 2.1

• Reasoning and Proof

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• Conditional is an if,then statement
• Two parts to a conditional statement
• Hypothesis the part of the statement that
  follows the word if
• Conclusion the part of the statement that
  follows the word then

Identify Hypothesis Conclusion

• If today is the first day of fall, then the month
  is September
• Hypothesis
• Conclusion

today is the first day of fall
the month is September
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Write a Conditional Statement

• A rectangle has four right angles

• If a figure is a rectangle, then it has four
  right angles

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Truth Value

• A conditional can have a truth value. A truth
  value identifies if the conditional statement is
  true or false.

What is the truth value?

• If it is February, then there are only 28 days in
  the month

• Truth value is False during Leap year there are
  29 days in the month of February

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Venn Diagrams

• Venn Diagrams can be used to show a conditional.

• The set of things that satisfy the hypothesis
  lies inside the set of things that satisfy the
  conclusion.

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Converse of a conditional

• The converse of a conditional switches the
  original hypothesis and conclusion.

Conditional If an animal is a dog, then it is a
Cocker Spaniel.
Converse If an animal is a Cocker Spaniel, then
it is a dog.
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Write the Converse

• If two lines are not parallel and do not
  intersect, then they are skew.

If two lines are skew, then they are not parallel
and do not intersect.
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Finding the truth value of a converse

• Conditional StatementIf a² 25, then a 5

What is the converse of this statement?
If a 5, then a² 25
True
What is the truth value of the converse?
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Check Understanding

• Write the statement all dogs are mammals as a
  conditional statement. Then write its converse.
  What is the truth value of each statement?

If an animal is a dog, then it is a mammal.
TRUE
If an animal is a mammal, then it is a dog.
FALSE
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Symbolism

• Conditional
• p q if
  p, then q
• Converse
• q p
• if q, then p

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Homework

• Page 71
• 2-34even, 40 - 48even, 54-58even, 59-61