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5.1.2. Definition of Π*
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Try these first
- 1.
Define a finite alphabet.
Hint
Think of the letters you can use in a language.
- 2.
What is a countable set?
Hint
Can you list all numbers? That is an example!
- 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.
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.
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.
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
4 more questions available
Enrol freeQuiz
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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Enrol freeChallenge 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