Problem 7. Let B = 1, 2, 3, 6, 12, 24, 36, 48. Define R on B...

Problem 7. Let B = {1, 2, 3, 6, 12, 24, 36, 48}. Define R on B by (x, y) is in R, if x divides y. a) List all the elements of R. b) Show that R is a partial order. c) Draw the Hasse diagram for R

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Transcript

00:01 Okay, so let's get started with part a of our exercise.

00:06 Okay, let's list the elements of r.

00:10 Well, when the first coordinate is 1, we are going to have 1 ,1, 1 ,2 and so on up to 1 ,48 because 1 divides everything.

00:32 Perfect.

00:33 Now, when the first coordinate is 2, we are going to have 2, 6, 12, 24, 36 and 48.

00:44 So, 2, 6, 2, 12 and so on up to 48.

00:52 Perfect.

00:53 Now, when the first coordinate is 3, we are going to have 3, 3.

01:00 Oh, here we need 2, 2.

01:04 Okay, perfect.

01:05 I was saying, now when the first coordinate is 3, we are going to have 3, 3, 3, 6 and so on up to 48.

01:22 Okay, now when the first coordinate is 6, we are going to have 6, 6, 6, 12 and so on up to 6, 48.

01:35 When the first coordinate is 12, we are going to have 12, 12, 12, 24, 12, 36 and so on up to 48.

01:52 Perfect.

01:52 When the first coordinate is 24, we are going to have 2 pairs only, 24, 24 and 24, 48.

02:07 Perfect.

02:08 When the first coordinate is 36, we are going to have 36, 36 only.

02:14 When the first coordinate is 48, we are going to have 48, 48 only.

02:23 Perfect.

02:24 Okay, this one was the first part of our exercise...

Question

Problem 7. Let B = {1, 2, 3, 6, 12, 24, 36, 48}. Define R on B by (x, y) is in R, if x divides y. a) List all the elements of R. b) Show that R is a partial order. c) Draw the Hasse diagram for R

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