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Consider the partial order with domain {3,5,6,7,10,14,20,30,60,70} and with x≤y if x evenly divides y. Select the correct Hasse diagram for the partial order

Consider the partial order with domain {3,5,6,7,10,14,20,30,60,70} and with x≤y if x evenly divides y. Select the correct Hasse diagram for the partial order

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.6: Quadratic Functions
Problem 57E
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Consider the partial order with domain {3,5,6,7,10,14,20,30,60,70} and with x≤y if x evenly divides y.

Select the correct Hasse diagram for the partial order

60 70 30 20 14 6 10 3 7 (b) Figure 3: A Hasse diagram shous a set of elements 3; 5; 6; 7; 10; 14; 20; 30; 60, 70. There are lines connecting 3 and 6, 6 and 30, 30 and 60, 5 and 10, 10 and 30, 10 and 20, 20 and 60, 10 and 70, 7 and 14, 14 and 70. LO
Transcribed Image Text:60 70 30 20 14 6 10 3 7 (b) Figure 3: A Hasse diagram shous a set of elements 3; 5; 6; 7; 10; 14; 20; 30; 60, 70. There are lines connecting 3 and 6, 6 and 30, 30 and 60, 5 and 10, 10 and 30, 10 and 20, 20 and 60, 10 and 70, 7 and 14, 14 and 70. LO
60 70 30 14 10 7 (a) Figure 2: A Hasse diagram shouws a set of elements 3; 5; 6; 7; 10; 14; 20; 30; 60, 70. There are lines conecting 3 and 6, 6 and 30, 30 and 60, 5 and 10, 10 and 20, 20 and 60, 10 and 70, 7 and 14, 14 and 70. 20
Transcribed Image Text:60 70 30 14 10 7 (a) Figure 2: A Hasse diagram shouws a set of elements 3; 5; 6; 7; 10; 14; 20; 30; 60, 70. There are lines conecting 3 and 6, 6 and 30, 30 and 60, 5 and 10, 10 and 20, 20 and 60, 10 and 70, 7 and 14, 14 and 70. 20
Expert Solution
Step 1

Step:-1

Given domain is 3, 5, 6, 7, 10, 14, 20, 30, 60, 70 with relation is x≤y if x divides y

Option (a):-

Advanced Math homework question answer, step 1, image 1

we can see 10≤30 and 10 divides 30 but there is no path between 10 and 30 to show this relation.

Hence, this is not correct graph.

Option (b):-

Advanced Math homework question answer, step 1, image 2

As, we can see for each path between two vertices, the given relation is satisfied.

So, this option (b) is correct.

 

 

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