Let denote a finite alphabet, * denote all words over that alphabet, and L denote the...
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Let denote a finite alphabet, * denote all words over that alphabet, and L denote the function that maps a string to its length, i.e. L: * N (where N denotes the natural numbers) [a] Is L partial, total, or both? [b] Is L one-to-one? onto? a bijection? [c] How many words in * have length n? [d] How many words in * have length s n [e] Explain whether * is finite, countable, or uncountable. [f] Explain whether P(Z*) - the set of all subsets over * -is finite, countable, or uncountable. Hint: how is this related to the real numbers in [0, 1). Let denote a finite alphabet, * denote all words over that alphabet, and L denote the function that maps a string to its length, i.e. L: * N (where N denotes the natural numbers) [a] Is L partial, total, or both? [b] Is L one-to-one? onto? a bijection? [c] How many words in * have length n? [d] How many words in * have length s n [e] Explain whether * is finite, countable, or uncountable. [f] Explain whether P(Z*) - the set of all subsets over * -is finite, countable, or uncountable. Hint: how is this related to the real numbers in [0, 1).
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Explanation of the Properties of the Function L and Sets a L is a total function A total function maps every element in its domain to exactly one elem... View the full answer
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