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Section 2-1 Conditional Statements

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If – Then Statements If the Lions lose this week, then they are going to be 0-5. This is a conditional statement The If: If the Lions lose this week, is the hypothesis The Then: Then they are going to be 0-5 is the conclusion

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Find the Hypothesis and Conclusion If Michigan beats Ohio State, then it will be an upset. Hypothesis: If Michigan beats Ohio State Conclusion: Then it will be an upset

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On your own Please construct your own If – Then conditional statement

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Writing a Conditional A tiger is an animal You can write this statement in two ways, which one makes sense. If it is a tiger, then it is an animal If it is an animal, then it is a tiger

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Try on your own Glass objects are fragile The correct way is: If it is a glass object, then it is fragile

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Counterexamples Counterexamples are one case which proves the entire statement false Example: I have the fastest car on Earth, the counterexample would be to find a faster car.

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Find the counterexample If it is fragile, then it is a glass object The counterexample would be a Polaris snowmobile, they are fragile, break easy, but are not glass.

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Find the counterexample If it is February, then there are only 28 days in this month Leap Year has 29 days in February

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Find the counterexample If you live in California, then you live in Los Angeles A person who lives in San Diego

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Venn Diagram A way to show a conditional statement visually. The hypothesis is inner circle and sits inside the set of things that satisfies the conclusion

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Example If I live in Fife Lake, then I live in Michigan

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Example Can you live in Michigan but not live in Fife Lake?

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Example Can you live in Fife Lake, but not live in Michigan?

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On your own Please construct a Venn diagram for the following conditional statement: If I live in Michigan then I cheer for the Lions.

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Converse Statements Rewriting the statement so the conclusion comes before the hypothesis Ex: If the Pistons win the championship then they are the best team in basketball. Hyp: If the Pistons win the championship Conclusion: Then they are the best team in basketball Converse: If the Pistons are the best team in basketball then they will win the championship

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On your own Write the converse to the statement: If I own an Arctic Cat then I have the fastest snowmobile.

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Answer If I own the fastest snowmobile, then I own an Arctic Cat

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