Explanation Given information: A = { 1 , 2 , 4 , 5 , 10 , 15 , 20 } . Concept used: Hasse Diagram: It is a mathematical diagram representing a partially ordered set with finite number or members involving transitive reduction. Calculation: The set has one minimal element 1 , so you can pick 1 . The beginning of the total order is 1 , with a total order of 1 . Set A 1 = A − { 3 } . You can indicate this by removing 1 from the Hasse diagram as shown below. Next, choose a minimal element from A 1 − { 1 } . Thus, there are two minimal elements 2 and 5 . Either one may be chosen, pick 5 . The total order thus far is total order 1 ≤ 5 . Set A 1 = A − { 1 } − { 5 } = A − { 1 , 5 }

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Author: EPP, Susanna S.

Publisher: Cengage Learning,

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Chapter 8.5, Problem 44ES

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A topological sorting for the “divides” relation on the set A={1,2,4,5,10,15,20}.

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Chapter 8.5, Problem 43ES

Chapter 8.5, Problem 45ES

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>tt 1:32 > trend.1m 1m (sales > summary(trend.1m) - tt) #3###23 (i) #### Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 2107.220 57.997 36.332e-16 *** tt -43.500 3.067 -14.18 7.72e-15 *** > trend = ts (fitted (trend.1m), start-start (sales), freq-frequency (sales)) sales trend ###23%23 (ii) #### as.numeric((1:32 %% 4) > X > q1 > q2 > q3 > 94 = = = = - as.numeric((1:32 %% 4) as.numeric((1:32 %% 4) as.numeric((1:32 %% 4) == 1) 2) == == 3) == 0) > season.lm = 1m (resid (trend.1m) 0+q1 + q2 + q3 + q4) #3##23%23 (iii) #### > summary(season.1m) Coefficients: Estimate Std. Error t value Pr(>|t|) q1 -38.41 43.27 -0.888 0.38232 92 18.80 43.27 0.435 0.66719 q3 -134.78 43.27 -3.115 0.00422 ** 94 154.38 43.27 3.568 0.00132 ** > season = ts (fitted (season.lm), start=start (sales), freq=frequency (sales)) > Y X season %23%23%23%23 (iv) #### >ar (Y, aic=FALSE, order.max=1) #23%23%23%23 (v) #### Coefficients: 1 0.5704 Order selected 1 sigma 2 estimated as 9431 > ar(Y, aic=FALSE,…

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A topological sorting for the “divides” relation on the set A = { 1 , 2 , 4 , 5 , 10 , 15 , 20 } .

Solution Summary: The author describes the Hasse diagram, which is a mathematical diagram representing the partially ordered set with finite number or members involving transitive reduction.

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To find:

A topological sorting for the “divides” relation on the set A={1,2,4,5,10,15,20}.

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Chapter 8 Solutions

A topological sorting for the “divides” relation on the set A = { 1 , 2 , 4 , 5 , 10 , 15 , 20 } .

Solution Summary: The author describes the Hasse diagram, which is a mathematical diagram representing the partially ordered set with finite number or members involving transitive reduction.

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To find: A topological sorting for the “divides” relation on the set A={1,2,4,5,10,15,20}.

Want to see the full answer?

Chapter 8 Solutions

To find:

A topological sorting for the “divides” relation on the set A={1,2,4,5,10,15,20}.