Of the 16 possible 2-input/1-output gates: * 8 of them are linear, in that the output is A xor (B and X) xor (C and Y). Any combination of these can only ever

Of the 16 possible 2-input/1-output gates: * 8 of them are linear, in that the output is A xor (B and X) xor (C and Y). Any combination of these can only ever generate linear combinations of their inputs, thus they cannot be universal. * 6 of them are monotonic, in that X op Y <= X' op Y' if X <= X' and Y <= Y'. Any combination of these can only ever generate monotonic functions of their inputs, thus they cannot be universal. * 4 gates (0, X, Y, 1) are both linear and monotonic. * The 6 gates which are neither linear nor monotonic are universal.