I I make a simple Boolean object 2 I apply a shader and it looks fine 3 If I apply a texture it looks wrong 4 When I look at the model in the modeling room I see triagles 5 How do I correct this Please see Diagram.

I believe you have to UV-map it after the boolean.

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Barbequed Pixels?

Your friendly neighborhood Wings3D nut.
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 Paul is correct. Carrara assigns a default UV map upon object creation based upon the geometry. Since booleans fundamentally alters the geometry, the UV map becomes useless be cause it is trying to map the old coordinates to the new geometry - which doesn't work.

This is true for all 3D software. 

To fix this issue, open the object in the vertex room and engage the UV mapping options. There you can realign the geometry to the UV space.

Thanks guys I got a result and I now know how to do it with in Carrara, Great!