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Show that. ............................

$\ (D_{10}, \leqslant)$ is a lattice. Draw its Hass's Diagram.


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We have $\ D_{10} = [1,2,5,10]$

The Hasse diagram is shown in

enter image description here

To show that $\ (D_{10}, \leqslant)$ = [1,2,5,10] are lattice. Now find 'V' & '^'

enter image description here

enter image description here

From the two table, we observe that every pair of element $\ D_{10}$ has LUB (least upper bound) and GLB (greatest upper bound). Hence ($\ (D_{10}, \leqslant)$) is a lattice.

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