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Let W denote the set of English words. For u, v ? W, declare u ?...

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Advance Math

Let W denote the set of English words. For u,v ? W, declare u ? v providedthat u, v have the same length and u,v have the same first letter and u, vhave the same last letter.

a) Prove that ? is an equivalence relation.

b) List all elements of the equivalence class [a]

c) List all elements of [ox]

d) List all elements of [are]

e) List all elements of [five]. Can you find more than 15?

f) Bonus. Find all three letter words x such that[x] has 5 elements.

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