Solution-What are the corresponding equivalence classes

What are the corresponding equivalence classes

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Reference no: EM131584749

Question: Consider the symbols ab...xyz AB...XYZ.

(a) Let α ∼1 β if the symbols α and β represent the same letter. Is ∼1 an equivalence relation? If so, what are the equivalence classes?

(b) Let α ∼2 β if the symbols α and β are the same case (upper or lower). Is ∼2 an equivalence relation? If so, what are the equivalence classes?

(c) Now assign a → 0, b → 1, . . . , z → 25, A → 26, . . . , Z → 51. Notice this converts our symbols to elements of Z52. If we apply ∼1, what are the corresponding equivalence classes in Z52? What happens if we instead apply ∼2?

(d) Challenge: Examine the equivalence classes of Z52 under each of ∼1 and ∼2. Do the classes themselves correspond to other familiar sets?

Reference no: EM131584749

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What are the corresponding equivalence classes

Reference no: EM131584749

Reference no: EM131584749

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