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5.1.2. Definition of Π*

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  1. 1.

    Define a finite alphabet.

    Hint

    Think of the letters you can use in a language.

  2. 2.

    What is a countable set?

    Hint

    Can you list all numbers? That is an example!

  3. 3.

    What defines a countable set?

    • Can be listed without omission
    • Contains infinite elements only
    • Random ordering
    Hint

    Recall the definition from the beginning of our lesson.

  4. 4.

    True or False: All substrings of a string form a countable set.

    • True
    • False
    Hint

    Think about how many parts make up a whole string.

  5. 5.

    Construct all possible valid programs of length 2 using a 3-character alphabet.

    Hint

    Focus on ensuring both start and end instructions are present.

  6. 6.

    Prove that the intersection of two countable sets is also countable.

    Hint

    Can you list pairs from both sets systematically?

Exercises

Total Questions

2

Estimated Time

4 min

Passing Score

70%

Instructions

  • Read each question carefully
  • You can use hints if you need help
  • Complete all questions before submitting

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Quiz

Total Questions

2

Estimated Time

4 min

Passing Score

70%

Instructions

  • Read each question carefully
  • You can use hints if you need help
  • Complete all questions before submitting

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Challenge Problems

Total Questions

2

Estimated Time

4 min

Passing Score

70%

Instructions

  • Read each question carefully
  • You can use hints if you need help
  • Complete all questions before submitting