Problem 5: Functions and Sets Let Σ denote a finite alphabet, Σ* denote all words over that alphabet, and L denote the function that maps a string to its length, i.e. L : Σ* → 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 Σ* have length n? [d] How many words in Σ* have length ≤ n [e] Explain whether Σ* is finite, countable, or uncountable. [f] Explain whether P(Σ*) - the set of all subsets over Σ* - is finite, countable, or uncountable. Hint: how is this related to the real numbers in [0, 1).
Problem 5: Functions and Sets Let Σ denote a finite alphabet, Σ* denote all words over that alphabet, and L denote the function that maps a string to its length, i.e. L : Σ* → 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 Σ* have length n? [d] How many words in Σ* have length ≤ n [e] Explain whether Σ* is finite, countable, or uncountable. [f] Explain whether P(Σ*) - the set of all subsets over Σ* - is finite, countable, or uncountable. Hint: how is this related to the real numbers in [0, 1).
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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Problem 5: Functions and Sets
Let Σ denote a finite alphabet, Σ* denote all words over that alphabet, and L denote the function that maps a string to its length, i.e. L : Σ* → 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 Σ* have length n?
[d] How many words in Σ* have length ≤ n
[e] Explain whether Σ* is finite, countable, or uncountable.
[f] Explain whether P(Σ*) - the set of all subsets over Σ* - is finite, countable, or uncountable. Hint: how is this related to the real numbers in [0, 1).
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