The Bryce 6 artists guides contains all the info you need regarding Booleans (for some reason I can't find the equivalent in the Bryce 7 guide). Here's the link:

http://documentation.daz3d.com/bryce/Bryce6ArtistGuide.htm

The Boolean operation is found by clicking on the attributes icon which is the 'A' in the list which appears with any primitive you create (see attached jpg). They are

Neutral

Positive

Negative

Intersect

Beginners tutorials for Bryce

Bryce Arena