Draw the Hasse Diagram of the following: 1. $D_{105}$ 2. $D

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Draw the Hasse Diagram of the following: 1.

$D_{105}$ 2.

$D_{72}$

written 8.3 years ago by

teamques10 ★ 69k

modified 3.2 years ago by

sagarkolekar ★ 11k

discrete mathematics

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1 Answer

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written 8.3 years ago by

teamques10 ★ 69k

I. We have 105= 3 x 5 x 7

Hence, 105 is the product of distinct prime number.

$D_{105}$ is a Boolean algebra.

$D_{105}$ = {1,3,5,7,15,21,35,105}

The Hasse diagram of $D_{105}$ is shown in the figure.

enter image description here

II.We have 72= 8 x 9

Hence, 72 is not the product of distinct prime number.

$D_{72}$ ={1,2,3,4,6,8,9,12,18,24,36,72}

The Hasse diagram of $D_{72}$ is shown in the figure.

enter image description here

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