`$$\bullet:=\lnot\circ$$`

`$$\circ:=\lnot\bullet$$`

`$$\bullet\oplus\bullet=\bullet$$`

`$$\circ\oplus\circ=\bullet$$`

`$$\bullet\oplus\circ=\circ$$`

`$$\bullet\otimes\bullet=\bullet$$`

`$$\bullet\otimes\circ=\bullet$$`

`$$\circ\otimes\circ=\circ$$`