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2-1 If-Then Statements; Converses

2-1 If-Then Statements; Converses. Examples. If it is lightning, then practice will be cancelled If it is 3:20, then school is over. If you have a daughter, then you are a parent If 2 lines intersect, then they do so at one point If 2 planes intersect, then they do so at a line.

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2-1 If-Then Statements; Converses

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  1. 2-1 If-Then Statements; Converses

  2. Examples • If it is lightning, then practice will be cancelled • If it is 3:20, then school is over. • If you have a daughter, then you are a parent • If 2 lines intersect, then they do so at one point • If 2 planes intersect, then they do so at a line.

  3. These statements are called IF-THEN statements, or more formally known as CONDITIONALS. If p, then q. Hypothesis Conclusion

  4. The words after IF and before THEN are part of the hypothesis. • The words after THEN are part of the conclusion • YOU DO NOT INCLUDE IF or THEN in either the hypothesis or the conclusion.

  5. Converse • Is created by interchanging the hypothesis and the conclusion • If it is 5th period, then it is lunch time. • If it is lunch time, then it is 5th period. ORIGINAL CONVERSE

  6. An if-then or conditional is false if an example can be found for which the hypothesis is true and the conclusion is false. When this happens, that example is called a COUNTEREXAMPLE • It takes only one counterexample to disprove a statement.

  7. If you live in Ohio, then you live in Lima. • Is this always true? • What is one counterexample?

  8. Converses and counterexamples • If you live in Lima, OH, then you live north of the Ohio River. • Write the converse. • Is it always true? • Give a counterexample

  9. Some conditionals have converses that are true. • If 2x = 30, then x = 15. • Find the converse, is it true?

  10. Conditionals are not always written with the “if” clause written first. Sometimes you will see the following • pimplies q. Means the same as ‘if p then q’ • ponly if q. Means the same as ‘if p then q’ • q if p. Means the same as ‘if p then q’ • THIS SLIDE WILL HELP YOU IN YOUR HOMEWORK WHEN YOU SEE QUESTIONS THAT DO NOT HAVE THE FORM OF “if p, then q”

  11. If a conditional and its converse are both true, then they can be combined into a single statement using the words “if and only if” • Abbreviated iff • These are called BICONDITIONALS

  12. Examples

  13. HWK • Pg. 35 • 1-10, 17-23,

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