let be the set of letters{a,b,.....z} Also, let (notice the superscript star in

Question

let be the set of letters{a,b,.....z} Also, let (notice the superscript star in its name) be the set of all finite string made of the letters for example "cat" epsilon , "dog" epsilon, "mathematics" epsilon (the empty string). We define a "permutation" relation p as follows P={(x,y) epsilon * times * /x is a permutation of y} it contains all the pairs of strings that are permutations of each other, for example ("flow", "wolf") epsilon P, ("teenager", "generate") epsilon P, ("player", "replay") epsilon P. Question: Is this relation P an equivalence relation or a partial order relation? (An equivalence relation is reflexive, symmetric, not antisymmetric, and transitive, and a partial order relation is reflexive, antisymmetric, not symmetric, and transitive). Prove your claim. Your argument does not have to be very formal, a good explanation in English should be sufficient.

Explanation / Answer

P is an equivalence relation because in a subset of (x,y), each x is a permutaion of y. All the letters in flow are present in wolf. All letters of teenager are present in generate and each letter in player is present in replay.

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