H Geometry 1.8.notebook - dozier math Geometry 1.8.notebook 1 August 28, 2013 1.7 p.42 #15, 812, 14...
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H Geometry 1.8.notebook 1 August 28, 2013 1.7 p.42 #15, 812, 14 2. a) definitions 4. a) Theorem b) Definition 6. Possible 8. Correct 10. Not correct, since we were reasoning from the converse. 12. Correct 14. Wendypurple monkey Katiered croc Jodygreen lizard
Transcript of H Geometry 1.8.notebook - dozier math Geometry 1.8.notebook 1 August 28, 2013 1.7 p.42 #15, 812, 14...
H Geometry 1.8.notebook
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August 28, 2013
1.7 p.42 #15, 812, 142. a) definitions 4. a) Theorem b) Definition
6. Possible 8. Correct
10. Not correct, since we were reasoning from the converse.
12. Correct 14. Wendypurple monkeyKatiered crocJodygreen lizard
H Geometry 1.8.notebook
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H Geometry 1.8.notebook
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1.8 Statements of Logic
Students will:State the inverse, converse, or contrapositive of a given statement.
p : hypothesisq : conclusionp q :Ifthen form
Logical Statements
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Theorem: If a conditional statement is true, then the contrapositive is also true
Rewrite the conditional statements in ifthen form. Then write the converse, inverse, and contrapositive of each and determine the truth of each statement.
Example:
a. Two segments with the same length are congruent.Conditional: If two segments have the same length, then they are congruent.
Converse: If two segments are congruent, then they are the same length.
Inverse: If two segments do not have the same length, then they are not congruent.
Contrapositve: If two segments are not congruent, then they don't have the same length.
b. A number divisible by 9 is also divisible by 3.
Conditional: If a number is divisible by 9, then it is also divisible by 3.
Converse: If a number is divisible by 3, then it is also divisible by 9.
Inverse: If a number is not divisible by 9, then it is also not divisible by 3.
Contrapositive: If a number is not divisible by 3, then it is also not divisible by 9.
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Chain Rule:
If p q and q r, then p r
Example:If the weather is nice on Friday, I will ride my bike. If I ride my bike, then I will go to see my friend.
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Example:Write a concluding statement for each of the following chains of reasoning.
a. c f g b a g b c
b. f ~h ~c f g ~c
c. ~m k h ~k m n
Example:Write a concluding statement for each of the following chains of reasoning.
a. c f g b a g b c
b. f ~h ~c f g ~c
c. ~m k h ~k m n
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Example:Write a concluding statement for the following chain of reasoning.
If gremlins grow grapes, then elves eat earthworms.
If trolls don't tell tales, then wizards weave willows.
If trolls tell tales, then elves don't eat earthworms.
Partner ProblemWrite a concluding statement for the following chain of reasoning.
If Susy is a Snooker, then Alfred is an Avixator.
If Alfred is an Avixator, then Johny is not a Jellygoon.
If Johny is not a Jellygoon, then Pam is a Powee.
If Pam is a Powee, then Ellie is an Ewelie.
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Homework:
1.8 p.47 #16, 8, 9
