PLEASE HELP ME! In each case, say whether or not R is a partial order on A . If

Question

PLEASE HELP ME!

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

Let R in case A be represented by R1.

Let R in case B be represented by R2.

Now, I am explaining it through an example for your easy help which will help you in solving your other problems as well in any you have.

(apple, apple) and (apple,atom) are each in both R1 and R2, but (atom, apple) is only in R2.

In the dictionary, "apple" comes before "atom". This explains R1.

In the alphabet, "a" comes at the same place as "a". This explains R2.

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.