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Math Help - class of equivalence

  1. #1
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    class of equivalence

    hello! i need help

    Suppose that R is a relation on the set of positive integers such that:
    aRb if and only if l(a) = l(b)

    where l(x) is the number of decimal digits of x. (for example l(122) is 3)

    we already proved that R is an equivalence relation..the question is:

    Considers the set of numbers formed from the 4 digits 1, 2, 3 and 4.
    What is the equivalence class of 12?

    thank you
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by qwerty321 View Post
    hello! i need help

    Suppose that R is a relation on the set of positive integers such that:
    aRb if and only if l(a) = l(b)

    where l(x) is the number of decimal digits of x. (for example l(122) is 3)

    we already proved that R is an equivalence relation..the question is:

    Considers the set of numbers formed from the 4 digits 1, 2, 3 and 4.
    What is the equivalence class of 12?


    thank you
    It is the set of all 2 digit numbers with digits selected from {1,2,3,4}

    CB
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  3. #3
    MHF Contributor

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    There are a total of 2^4= 16 two digit numbers in that set.

    Here are four of them: 11, 12, 13, 14.
    Can you find the other twelve?
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