how to reverse the logical operator AND, if I have:

(A AND B) XOR C = D

how to get: A

There are only 16 combination of four boolean variables, so it is easy to prove that

**A** is not an unequivocal function of

**B,C,D**:

`A B C D (A&B) (A&B)^C ((A&B)^C)=D`

0 0 0 0 0 0 1

~~0 0 0 1 0 0 0~~

~~0 0 1 0 0 1 0~~

0 0 1 1 0 1 1

0 1 0 0 0 0 1

~~0 1 0 1 0 0 0~~

~~0 1 1 0 0 1 0~~

0 1 1 1 0 1 1

1 0 0 0 0 0 1

~~1 0 0 1 0 0 0 ~~

~~1 0 1 0 0 1 0~~

1 0 1 1 0 1 1

~~1 1 0 0 1 1 0~~

1 1 0 1 1 1 1

1 1 1 0 1 0 1

~~1 1 1 1 1 0 0~~

Variable

** A** is

*false* when

**B,C,D** is 0,0,0 or 0,1,1 or 1,0,0 or 1,1,1.

Variable

** A** is

*true* when

**B,C,D** is 0,0,0 or 0,1,1 or 1,0,1 or 1,1,0.