A new method for Logic Gate Arithmetic is proposed allowing sets to be added, subtracted, multiplied, and divided in an entirely new way leading to an alternate and expanded appreciation of Set Theory. 11 new Logic Operators are derived from the known Logic Operators: AND, OR, NOR, XOR, and XNOR and their relationships are described extensively. Utilising the principles of Dimensional Gate Operators (DGO), the new operators are shown to be directly related to dimensionality, both higher and lower, and the relationship to the Quaternions is given a fledgling treatment.