EXAMPLE 2.1.1*
In order for the statement "All of the cancer has been removed" to be FALSE, there must be at least one small particle of cancer that wasn't removed. Since there was never any cancer to begin with, there can't be any cancer that wasn't removed. For this reason, the statement is vacuously TRUE. The surgeons didn't lie, although they may have been somewhat less candid than we would like them to be.

On the other hand, if the surgeons had said "Some of the cancer has been removed," they would have have lied, since this statement means "At least one (cancer cell) was removed."