Please do (4) & (5) only for Exercise 4.15. I have included 4.13 and 4.14 for your reference as well. And please keep it short and simple with typefont or legible handwriting, and clear explanations for each step. Thank you! Example 4.13. Consider a set with three elements, S = {a,b, c}. SetA = {(a,a), (b, b), (c, c)}. Essentially, up to permuting the names of theelements, there are 5 partial orders R on S:(1) The elements are linearly ordered:R= Au {(a,b), (a, c), (b, c)}.(2) One element is greater than the two other unrelated elements:R = Au {(b, a), (c, a)}.(3) One element is smaller than the two other unrelated elements:R = Au {(a, b), (a, c)}.(4) Two elements are related, while the third element is unrelated:R= Au {(a,b)}.(5) The elements are not related:R = A.Exercise 4.14. Display each of the partial orders in the three element ex-ample graphically. Decide whether there are minimal or maximal elements,and if so, name them. Decide whether the partial orders have minima ormaxima, and if so, name them.Exercise 4.15. Repeat Example 4.13 and Exercise 4.14 with a set of fourelements.

Name: Please do (4) & (5) only for Exercise 4.15. I have included 4.13 and 4
Uploaded: 2024-03-20T06:38:44.000Z
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Description: Please do (4) & (5) only for Exercise 4.15. I have included 4.13 and 4.14 for your reference as well. And please keep it short and simple with typefont or legible handwriting, and clear explanations for each step. Thank you! Example 4.13. Consider a