Let W denote the set of English words. For u, v E W, declare u~ v provided that u, v have the same length and u, v have the same first letter and u, v have 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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