Operator Base for XOR and AND

Question

How can I form a complete operator base from XOR and AND?

a and b = a and b

a or b = (a xor b) xor (a and b)

but I can't find a solution for NOT

Thanks for your help

Answer 1

¬a = a ⊕ 1  

Using other notation,  not a = a xor 1

Comments

And the 1 is needed as a constant since you cannot express not with {and, xor} alone. That is why the Reed-Muller form has the additional xor with 1 to express negation.