Recall the definition of alphabet E and string over an alphabet. Let ɛ be the empty string. The following rules recursively define a set S of strings over the alphabet E = {0, 1}: Basis step : the empty string in S, i.e., e S. Inductive step : if x E S is a string in S, then Ox1 is a string in S, i.e., Ox1 E S. Describe without using recursion, the set of strings in S. The suggested way is to first give a few examples of strings in S, and then describe in plain English the structure of all and only the strings in S. Important: your description must separate the strings in S from the strings not in S. If you say something like, “S is a set of strings made of Os and 1s," you are not making an incorrect statement, but the answer is not acceptable because there are many strings made of Os and 1s that are not in S.

Recall the definition of alphabet E and string over an alphabet. Let ɛ be the empty string. The following rules recursively define a set S of strings over the alphabet E = {0, 1}: Basis step : the empty string in S, i.e., e S. Inductive step : if x E S is a string in S, then Ox1 is a string in S, i.e., Ox1 E S. Describe without using recursion, the set of strings in S. The suggested way is to first give a few examples of strings in S, and then describe in plain English the structure of all and only the strings in S. Important: your description must separate the strings in S from the strings not in S. If you say something like, “S is a set of strings made of Os and 1s," you are not making an incorrect statement, but the answer is not acceptable because there are many strings made of Os and 1s that are not in S.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.4: Binary Operations

Problem 3E

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