Hasse Diagram for Cartesian Product of Three Sets

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I have to draw Hasse diagram for three sets in the picture.

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Is my drawing correct?

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Notice that this is an extended version of the cube $\mathbf2\times\mathbf2\times\mathbf2$ which you can find right at the beginning the following wikipedia page: Power set.

In your case, the product is $\mathbf2\times\mathbf2\times\mathbf3$, so you have to extend one dimension by one unit, like so:

enter image description here