I need help with this problem involving preorders and partial orders R.4. Consider the relation R = {(f, g): f, g:R → R& f(2) < g(2)}. (The notation used hereindicates that fand g are functions with domain the set of all real numbers and range a subset ofthe set of real numbers.) Show that R defines a preorder on the set of real functions, but it doesnot define a partial order on the set of real functions.

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Answered: R.4. Consider the relation R = {(f, g):…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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The figure below is a Hasse diagram for a partial order: A H. C F What are the minimal elements? O E O E, D, H O E, D, F, H O E, D
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Q3. A project manager must select four analysts from her group to write four different software functions. There are 4 junior and 5 senior analysts in her group. The first and fourth functions can be written by any of the analysts. The second function must be written by a senior person and the third function must be written by a junior person. How many ways are there for her to assign the analysts to the functions if no person can be assigned to more than one function?
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Suppose we want to choose 6 objects, without replacement, from 9 distinct objects. (If necessary, consult a list of formulas.) (a) How many ways can this be done, if the order of the choices matters? ☐ (b) How many ways can this be done, if the order of the choices does not matter? ☐
Suppose we want to choose 7 objects, without replacement, from 11 distinct objects.(If necessary, consult a list of formulas.) (a) How many ways can this be done, if the order of the choices is taken into consideration? (b) How many ways can this be done, if the order of the choices is not taken into consideration?
8ab please
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