Short human descriptions for logic's AND, OR and NOT

In a user interface, we are offering the user to combine searches using either AND, OR or NOT

http://whatis.techtarget.com/definition/logic-gate-AND-OR-XOR-NOT-NAND-NOR-and-XNOR

We have little graphics explaining the effect, but what would be good, laymen, human words to describe these operations in english as separate items in a menu list ? Short sentences like 'combine searches','intersect searches','exclude from previous search' spring to mind .. but I'm not a native speaker.

It would depend to an extent on your target audience (Children?, Mathematicians?)

AND - Must also include

OR - May instead include

NOT - Must not include

Try this:

AND - "all"

OR - "at least one"

NOT - "opposite"

XOR - "odd number"

NAND - "not all"

NOR - "nothing"

XNOR - "all or nothing"