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28 July, 12:01

What are the equivalence classes of these bit strings forthe equivalence relation in Exercise 11? a) 010b) 1011c) 11111d) 01010101

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Answers (2)
  1. 28 July, 13:47
    0
    d) 01010101
  2. 28 July, 15:50
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    [010]_{R} = the first three bits of s are 010 [1011]_{R} = the first three bits of s are 101 [11111]_{R} = s ∈ A [01010101]_{R} = the first three bits of s are 010

    Explanation:

    We say ∼ is an equivalence relation on a set A if it satisfies the following three properties:

    a) reflexive: for all a∈A, a∼a.

    b) symmetry: for all a, b∈A, if a∼b then b∼a.

    c) transitivity: for all a, b, c∈A, if a∼b and b∼c then a∼c.

    Given

    A = Set of all bit strings that have a length of at least 3

    R = { (x, y) first three bit of x and y are same

    a) the equivalence classes of 010 will contain all bit strings that have as the first three digits 010

    [010]_{R} = the first three bits of s are 010

    b) the equivalence classes of 1011 will contain all bit strings that have as the first three digits 101

    [1011]_{R} = s ∈ A

    c) the equivalence classes of 11111 will contain all bit strings that have as the first three digits 111

    [11111]_{R} = the first three bits of s are 111

    d) the equivalence classes of 01010101 will contain all bit strings that have as the first three digits 010

    [01010101]_{R} = s ∈ A
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