In each case, say whether or not R is a partial order on A . If so, is it a tota
ID: 3007474 • Letter: I
Question
In each case, say whether or not R is a partial order on A. If so, is it a total order?
(a) A = the set of all words of English, R = {(x, y) A × A | the word y occurs at least as late in alphabetical order as the word x}.
(b) A = the set of all words of English, R = {(x, y) A × A | the first letter of the word y occurs at least as late in the alphabet as the first letter of the word x}.
(c) A = the set of all countries in the world, R = {(x, y) A × A | the population of the country y is at least as large as the population of the country x}.
Explanation / Answer
(a}R is Partially ordered Set as well as Totally ordered. (b)R is neither Partilly ordered nor Totally ordered. (c)R is Partially ordered but not Totally ordered.
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