Let A be a partially ordered set, called “the alphabet.” Let W be the set of all “words” of length two—that is, all permutations of two letters of the alphabet. Define the relation ≤ on W as follows: for x1x2 ∈ W and y1y2 ∈ W, (i) x1 < y1 = y1 or (ii) x1 = y1 and x2 ≤ y2.Prove that ≤ is a partial ordering for W (called the lexicographic ordering, as in a dictionary).
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