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Understanding Conditional Statements: Hypothesis, Conclusion, and Counterexamples

Learn about conditional statements, including the hypothesis, conclusion, counterexamples, and Venn diagrams. Explore examples and how to construct statements for logical reasoning.

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Understanding Conditional Statements: Hypothesis, Conclusion, and Counterexamples

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  1. Section 2-1 Conditional Statements

  2. 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

  3. 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

  4. On your own • Please construct your own If – Then conditional statement

  5. 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

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

  7. 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.

  8. 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.

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

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

  11. 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

  12. Example • If I live in Fife Lake, then I live in Michigan

  13. Example • Can you live in Michigan but not live in Fife Lake?

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

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

  16. 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

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

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

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