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Can someone check this for me? (Equivalence classes)

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  1. Oct 18, 2014 #1
    • This thread is missing the Homework Template due to originally being posted in another forum.
    Question: Find the equivalence classes and the number of equivalence classes of the following relations.

    A is the set of all possible strings of 3 or 4 letters in alphabet {A, B, C, D}, and (x, y) ∈ R if and only if x and y have the same first letter and the same third letter.



    My attempted answer: A_B_, A_C_, A_D_, B_A_, B_C_, B_D_, C_A_, C_B_, C_D_, D_A_, D_B_, D_C_.
    This would be 12 different classes.

    Is this correct or am I missing something?
     
  2. jcsd
  3. Oct 19, 2014 #2
    There is typically no restriction on strings containing repeat letters. Other than that, this looks fine.
     
  4. Oct 21, 2014 #3
    Awesome thanks :)
     
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