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Section 33.9 Practice Exercises

Day One

1

Put each set into normal form and prime form.

Answer
  1. Normal form is [0, 2, 7]. Prime form is (027).

  2. Normal form is [1, 3, 6, 8]. Prime form is (0257).

  3. Normal form is [6, 10, 11, 1]. Prime form is (0137).

  4. Normal form is [7, 8, 0, 3]. Prime form is (0158).

  5. Normal form is [11, 0, 1, 4, 6]. Prime form is (01257).

  6. Normal form is [6, 7, 10, 11, 2]. Prime form is (01457).

  7. Normal form is [9, 10, 0, 1, 4, 6]. Prime form is (013479).

Day Two

2

For each of the six sets in the example below, determine the normal form, prime form, Forte number, and interval vector.

Answer
Set Normal Form Prime Form Forte Number Interval Vector
1 [11, 1, 3, 5, 6] (01357) 5–24 131221
2 [5, 8, 10, 0] (0247) 4–22 021120
3 [9, 0, 1, 4, 5] (01458) 5–21 202420
4 [3, 5, 6, 10] (0237) 4–14 111120
5 [2, 3, 6, 7, 9, 10] (013478) 6–Z19 313431
6 [2, 3, 5, 6, 9, 10] (013478) 6–Z19 313431
Table 33.9.1

Day Three

3

Transposition (T\(\text{}_{n}\)) of Sets. Transpose the following sets as specified.

  1. Transpose [3, 6, 7] at T\(\text{}_{2}\): [ , , ]

  2. Transpose [2, 4, 8, 9] at T\(\text{}_{7}\): [ , , , ]

  3. Transpose [1, 2, 4, 7, 8] at T\(\text{}_{9}\): [ , , , , ]

Answer
  1. [5, 8, 9]

  2. [9, 11, 3, 4]

  3. [10, 11, 1, 4, 7]

4

Inversion (T\(\text{}_{n}\)I) of Sets. Invert the following sets. Write your answers in normal form.

  1. Invert [7, 10, 11] at T\(\text{}_{0}\)I: [ , , ]

  2. Invert [0, 2, 4] at T\(\text{}_{4}\)I: [ , , ]

  3. Invert [4, 6, 10, 11] at T\(\text{}_{9}\)I: [ , , , ]

Answer
  1. [1, 2, 5]

  2. [0, 2, 4]

  3. [10, 11, 3, 5]

5

Specify the interval of inversion from the first set to the second set.

  1. [2, 4, 7] inverts to [3, 6, 8] at what T\(\text{}_{n}\)I?

  2. [1, 2, 4, 7] inverts to [4, 7, 9, 10] at what T\(\text{}_{n}\)I?

  3. [6, 7, 10, 1, 2] inverts to [3, 4, 7, 10, 11] at what T\(\text{}_{n}\)I?

Answer
  1. T\(\text{}_{10}\)I

  2. T\(\text{}_{11}\)I

  3. T\(\text{}_{5}\)I

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