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    String Proof and Discrete Math Word

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    A set S of bit strings is defined in the following way:
    1. the empty string is an element of S
    2. 0x1 is an element of S if x is an element of S.

    a. List five specific elements of S.
    b. List strings, if any, of length six which are elements of S.
    c. Prove or disprove that there are no strings of length eleven is S.

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    Solution Preview

    a. List five specific elements of S.

    By the properties 1), we know that

    I) the empty string is in S;

    Then by 2), we know that

    II) 01 is in S;

    Keeping applying 2), we know that

    III) 0011 is in S;

    IV) 000111 is in S;

    V) ...

    Solution Summary

    The following posting provides an example of working with strings and a proof.