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2.1 Conditional Statements

2.1 Conditional Statements. 10/2. Learning Targets. I can find the truth value given a conditional and a converse I can rewrite a statement as a conditional and write the conditional’s converse . If-Then Statements.

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2.1 Conditional Statements

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  1. 2.1 Conditional Statements 10/2

  2. Learning Targets • I can find the truth value given a conditional and a converse • I can rewrite a statement as a conditional and write the conditional’s converse.

  3. If-Then Statements • Ex: If you spend more time studying for the exam, then you will get a better grade. • Conditional – Another name for an if-then statement; has two parts…the part following if is the hypothesis, and the part following then is the conclusion

  4. If-Then Statements • Ex: If you spend more time studying for the exam, thenyou will get a better grade. • Hypothesis: • you spend more time studying for the exam. • Conclusion: • you will get a better grade.

  5. Identifying the Hypothesis and Conclustion • If today is the first day of fall, then the month is September. • If y – 3 = 5, then y = 8 • If two lines are parallel, then the lines are coplanar.

  6. Writing a Conditional • You are taking a sentence and rewriting it in if-then form.

  7. Writing a Conditional • An integer that ends with 0 is divisible by 5. • If an integer ends with 0, then it is divisible by 5

  8. Practice • An acute angle measures less than 90 degrees. • A square has four congruent sides. • Two skew lines do not line in the same plane.

  9. Truth Value • Every conditional has a truth value. • The truth value is either true or false. • True - it has to be true all of the time. • False - you need to provide just one counterexample(an example that proves a statement false).

  10. Finding Counterexamples • If it is February , then there are only 28 days in the month. • If x² ≥ 0, then x ≥ 0.

  11. Converse • The converse of a conditional switches the hypothesis and conclusion. • So… If THIS, then THAT becomes If THAT, then THIS

  12. Writing Converses • EX : • Conditional: If two lines intersect to form right angles, then they are perpendicular. • Converse: If two lines are perpendicular, then they intersect to form right angles.

  13. You try… • Conditional : If x = 9, then x + 3 = 12 • Converse: __________________

  14. Truth values with Converses • If a conditional is true, it doesn’t necessarily mean the converse is true also. You need to be able to determine: 1) is a conditional true or false, and 2) is the converse true or false

  15. Example: If a figure is a square, it has four sides. Step 1) Determine if the conditional is true or false. Yes, it is true. Step 2) write its converse. If a figure has four sides, then it is a square. Step 3) Determine the truth value. Remember, if it is false, you must provide a counterexample. False, a Rectangle

  16. Try: Conditional: If x² = 25, then x = 5 Truth Value of Conditional: Converse: Truth Value of Converse:

  17. Conditional: If x = 2, then = 2 • Write the converse and find the truth values for both the conditional and converse.

  18. Symbolic Form • Conditional pq (If p, then q) • Converse qp (if q, then p)

  19. 2-1 Packet • #1-13

  20. Homework • P. 71 #3-31 odd, 43, 45, 47

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