From $A+B=1$ and $AB=0$ we get either of $A,B$ is $1$ and another is $0$
Now, $AC=BC$, here $C$ has to be $0$ (because $A,B$ has different values)
$C=0$
Now, $A+C=1$
So, $A=1$ and $AB=0$ so, $B=0$
So, we get:
$A=1$ , $B=0$ , $C=0$
These are the values.