a) Consider the whole of the English words set. Suppose an English word x is related to another English word y if x and y begin with the same letter. i) Show that this is an equivalence relation. ii) Compute C(quadratic) and C(rhombus) iii) How many equivalence classes are there in all, and why? iv) What is the partition of the English words under this relation? b) Consider Z, the set of integers. Suppose we define the relation: x is related to y if x - y > 3, x, y 0 Z. Determine whether or not the relation is i) reflexive ii) symmetric

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Q: And what would be the 15 equivalence relations? And what does "up to isomorphism" mean?

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Q: . How many equivalence relations are there on the set S = {1, 2, 3, 4, 5}? 15 45 60 52

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A: That's easy. Have a great day!!!

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