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2.3– Conditional Statements

2.3– Conditional Statements. Logic. Conditional Statement (conditionals) A statement that contains “if” and “then” Hypothesis (p) – the portion after “if” Conclusion (q) – the portion after “then” p  q (If p then q ) (read p implies q ). Conditional Example.

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2.3– Conditional Statements

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  1. 2.3– Conditional Statements

  2. Logic • Conditional Statement (conditionals) • A statement that contains “if” and “then” • Hypothesis (p) – the portion after “if” • Conclusion (q) – the portion after “then” • p  q (If p then q) (read pimplies q)

  3. Conditional Example • If a car is a Corvette, then it is a Chevrolet. • Hypothesis (p) – “a car is a Corvette” • Conclusion (q) – “it is a Chevrolet”

  4. Leonhard Euler (1707-1783) • Swiss mathematician

  5. Then If Euler Diagrams • Euler Diagram (“Oiler”) • A type of diagram that shows logical relationships • The hypothesis goes in the circle, the conclusion goes in the rectangle • Venn Diagrams

  6. Chevrolet Corvette Euler Diagrams • If a car is a Corvette, then it is a Chevrolet.

  7. You are Dead. Ninja Present Euler Diagrams • If a Ninja is present, Then you are most likely dead.

  8. Brilliant People. “Other” People. South Carolina and UGA Fans Clemson Fans Euler Diagrams • If you are a Clemson fan, Then you are brilliant.

  9. CONVERSE • Converse • Switch the hypothesis and conclusion • q  p (q implies p) (If it is a Chevrolet, then it is a Corvette.)

  10. Counterexample • An example that proves a statement FALSE If it is a Chevrolet, then it is a Corvette. Counterexamples: Impala, Tahoe, Silverado, etc.

  11. Birds have wings. • Conditional: • If it is a bird, then it has wings. • Identify the hypothesis: • it is a bird • Identify the conclusion: • it has wings

  12. If it is a bird, then it has wings. • Write the converse: • If it has wings, then it is a bird. • Is this true or false? • Counterexamples? • airplane, vampire (bat), Mothman

  13. Inverse • Inverse of a statement is formed by negating both the Hypothesis and the conclusion. ~p~q Ex) If it is not a bird, then it doesn’t have wings.

  14. Contra positive • Contra positive is formed by negating the Converse. ~q~p Ex) If it does not have wings, then it is not a bird.

  15. Logical Equivalents • Any two statements with the same truth value are called, Logical Equivalents. • Conditional Statement and Contra positive are Logical Equivalents. • Converse and Inverse are also Logical Equivalents.

  16. Logical Chains • Logical Chains • Linking together conditionals in a logical order • It does not matter if the conditionals are true but they MUST be linked logically

  17. Logical Chains • Correct • If sirens shriek, then dogs howl. • If dogs howl, then cats freak out. • If cats freak out, then mice go crazy. • Conclude: If sirens shriek, then mice go crazy.

  18. Logical Chains • Incorrect • If dogs howl, then cats freak out. • If sirens shriek, then dogs howl. • If cats freak out, then mice go crazy. • This is incorrect because the conclusions and hypotheses don’t match up

  19. Create Your Own Logical Chain • First Hypothesis: “If I fail Geometry Class, then I will not graduate from high school.

  20. Create Your Own Logical Chain • If I don’t graduate from high school, Then Florida State will be the only University to accept me.

  21. Create Your Own Logical Chain • If Florida State is the only University to accept me, Then I will go there.

  22. Create Your Own Logical Chain • If Florida State is the only University to accept me, Then I will go there.

  23. Create Your Own Logical Chain • If I go to Florida State, Then my “degree” will be written on toilet paper and thus, will be worthless.

  24. Create Your Own Logical Chain • If my “degree” is written on toilet paper and thus worthless, then I will be unable to get a job.

  25. Create Your Own Logical Chain • If I am unable to get a job, Then I will become a transient miscreant.

  26. Practice • Write a conditional statement given the facts below. • Congruent Angles have the same measure. • Squares are parallelograms. • Sandy’s next door neighbor’s name is Carl.

  27. Practice • Given the Conditional Statement below, write the converse, inverse and contra positive statements. Then determine the Truth Value for all four statements and provide counter examples for any False statements. • If an angle measures 35 degrees, Then it is acute.

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