It is known that the third quandle homology group $H_3^Q(R_3;\mathbb{Z}) \cong \mathbb{Z}_3$. Each colouring $C$ of a knot diagram by a dihederal quandle $R_3$ induces a homomorphism $f:C \rightarrow \mathbb{Z}_3$.
Let a knot diagram be given and coloured by a dihederal quandle $R_3=\{0,1,2\}$. Let us denote this fixed colouring by $C$. Suppose also that $f(C)={1}$. Let $c \subset C$,then can we say that $f(c)=1$ as well.