48. Multiple Representations You have illustrated true conditional statements with Venn diagrams. You can do the same thing with true biconditionals. Consider the following statement.

    An integer is divisible by 10 if and only if its last digit is 0.

    1. Write the two conditional statements that make up this biconditional.
    2. Illustrate the first conditional from part (a) with a Venn diagram.
    3. Illustrate the second conditional from part (a) with a Venn diagram.
    4. Combine your two Venn diagrams from parts (b) and (c) to form a Venn diagram representing the biconditional statement.
    5. What must be true of the Venn diagram for any true biconditional statement?
    6. Reasoning How does your conclusion in part (e) help to explain why you can write a good definition as a biconditional?

Standardized Test Prep

SAT/ACT

49. Which statement is a good definition?
    1. Rectangles are usually longer than they are wide.
    2. Squares are convex.
    3. Circles have no corners.
    4. Triangles are three-sided polygons.
50. What is the exact area of a circle with a diameter of 6 cm?
    6. 28.27 cm
    7. 9 π  m 2 9 pi , m squared
    8. 36 π  cm 2 36 pi , cm squared
    9. 9 π  cm 2 9 pi , cm squared

Extended Response

51. Consider this true conditional statement.

    If you want to buy milk, then you go to the store.

    1. Write the converse and determine whether it is true or false.
    2. If the converse is false, give a counterexample to show that it is false. If the converse is true, combine the original statement and its converse as a biconditional.

Mixed Review

See Lesson 2-2.

Write the converse of each statement.

52. If you do not sleep enough, then your grades suffer.
53. If you are in the school chorus, then you have a good voice.
54. Reasoning What is the truth value of the contrapositive of a true conditional?

Get Ready! To prepare for Lesson 2-4, do Exercises 55–57.

See Lesson 2-1.

What are the next two terms in each sequence?

55. 100, 90, 80, 70,…
56. 2500, 500, 100, 20,…
57. 1 , 2 , 0 , 3 , − 1 , … 1 comma 2 comma 0 comma 3 comma negative 1 comma dot dot dot

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