C Challenge

31. Biology Consider the following given statements and conclusion.

    Given: If an animal is a fish, then it has gills.

    A turtle does not have gills.

    You conclude: A turtle is not a fish.

    1. Make a Venn diagram to illustrate the given information.
    2. Use the Venn diagram to help explain why the argument uses good reasoning.
32. Reasoning Use the following algorithm: Choose an integer. Multiply the integer by 3. Add 6 to the product. Divide the sum by 3.
    1. Complete the algorithm for four different integers. Look for a pattern in the chosen integers and in the corresponding answers. Make a conjecture that relates the chosen integers to the answers.
    2. Let the variable x represent the chosen integer. Apply the algorithm to x. Simplify the resulting expression.
    3. How does your answer to part (b) confirm your conjecture in part (a)? Describe how inductive and deductive reasoning are exhibited in parts (a) and (b).

Standardized Test Prep

SAT/ACT

33. What can you conclude from the given true statements?

    If you wake up late, then you miss the bus.

    If you miss the bus, then you are late for school.

    1. If you are late for school, then you missed the bus.
    2. If you wake up late, then you are late for school.
    3. If you miss the bus, then you woke up late.
    4. If you are late for school, then you woke up late.

Short Response

34. Claire reads anything Andrea reads. Ben reads what Claire reads, and Claire reads what Ben reads. Andrea reads whatever Dion reads.
    1. Claire is reading Hamlet. Who else, if anyone, must also be reading Hamlet?
    2. Exactly three people are reading King Lear. Who are they? Explain.

Mixed Review

See Lesson 2-3.

35. Write the following definition as a biconditional.

    Inductive reasoning is reasoning based on patterns you observe.

Get Ready! To Prepare for Lesson 2-5, do Exercises 36–39.

See Lessons 1-4 and 1-5.

Use the figure below.

36. Name ∠ 1 angle 1  in two other ways.
37. Name ∠ 2 angle 2  in two other ways.
38. If ∠ 1 ≅ ∠ 2 , angle 1 approximately equal to angle 2 comma  name the bisector of ∠ A O C . angle eh o c .

39. Classify ∠ A O C . angle eh o c .

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