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Draw the Hasse Diagram of the following: 1. $D_{105}$ 2. $D_{72}$
1 Answer
written 7.7 years ago by |
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.
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.