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Math Help - Equivalence classes (Discrete Math)

  1. #1
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    Equivalence classes (Discrete Math)

    Here's the original problem:
    ------------------------------------
    Let R be the relation congruence modulo 4. which of the following equivalence classes are equal?
    [7], [-3],[5],[-27],[32],[-14],[243],[9]
    -------------------------------------

    I first began the problem by setting up four classes: 0, 1, 2, and 3. I then divided each number, for example 7 divided by 4 which yielded a remainder 3. So, 7 would be in class 3. I know how to do the positive numbers, but how would I go about doing the negative?
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  2. #2
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    Hello, Don!

    Let R be the relation congruence modulo 4.
    Which of the following equivalence classes are equal?
    [7], [-3], [5],[-27], [32], [-14], [243], [9]

    I first began the problem by setting up four classes: 0, 1, 2, and 3. . . . . Good!
    I then divided each number, for example 7 divided by 4 which yielded a remainder 3.
    So, 7 would be in class 3. . . . . Right!

    I know how to do the positive numbers, but how would I go about doing the negative?

    Use the same procedure.
    If you get a negative remainder, use the modulo to "make it positive".


    For example: . (-27) \div 4 \:=\:-6,\;{\color{blue}\text{rem.}-3}

    . . And we know that: . -3 \:\equiv\: 1 \pmod{4}

    . . Therefore: . [-27] \:=\:[1]

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  3. #3
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    Thanks for the help. Would it be necessary for me to draw a binary relation or would it not matter?
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