B Apply

Write each statement as a conditional.

25. “We're half the people; we should be half the Congress.”—Jeanette Rankin, former U.S. congresswoman, calling for more women in office
26. “Anyone who has never made a mistake has never tried anything new.”—Albert Einstein
27. Probability An event with probability 1 is certain to occur.

28. Think About a Plan Your classmate claims that the conditional and contrapositive of the following statement are both true. Is he correct? Explain.

    If x = 2 , x equals , 2 comma  then x 2 = 4 . x squared , equals 4 .

    • Can you find a counterexample of the conditional?
    • Do you need to find a counterexample of the contrapositive to know its truth value?
29. Open-Ended Write a true conditional that has a true converse, and write a true conditional that has a false converse.

30. Multiple Representations Write three separate conditional statements that the Venn diagram illustrates.

    

31. Error Analysis A given conditional is true. Natalie claims its contrapositive is also true. Sean claims its contrapositive is false. Who is correct and how do you know?

Draw a Venn diagram to illustrate each statement.

32. If an angle measures 100, then it is obtuse.
33. If you are the captain of your team, then you are a junior or senior.
34. Peace Corps volunteers want to help other people.

Algebra Write the converse of each statement. If the converse is true, write true. If it is not true, provide a counterexample.

35. If x = − 6 , x equals negative 6 , comma  then | x | = 6 . vertical line x vertical line equals 6 .
36. If y is negative, then −y is positive.
37. If x < 0 , x less than , 0 comma  then x 3 < 0 . x cubed , less than 0 .
38. If x < 0 , x less than , 0 comma  then x 2 > 0 . x squared , greater than 0 .
39. Advertising Advertisements often suggest conditional statements. What conditional does the ad below imply?

Write each postulate as a conditional statement.

40. Two intersecting lines meet in exactly one point.
41. Two congruent figures have equal areas.
42. Through any two points there is exactly one line.

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