Henceforth, XAND is the first kind of XAND defined to realize minterm 1.
XNAND is defined as the complement of XAND. Therefore,
A XAND B = A AND NOT B
.:
A XNAND B = B OR NOT A
.: the set of all dual-input binary gates are:
0
A AND B
A XAND B
A
B XAND A
B
A XOR B
A OR B
A NOR B
A XNOR B
NOT B
A XNAND B
NOT A
B XNAND A
A NAND B
1
Thus XAND and XNAND lack reflexivity.
The nth kind of exclusive-and gate realizes mintern n, so it must have ceil(lg(n)) or more inputs, with the unused msbs tied low. In for this purpose, A above is the lsb.