Question about long exact sequences and homology

I have a question about Hatcher's chapter on long exact sequences (page 116, right before theorem 2.16). I'll rewrite the bit I don't understand.

Let $X$ be a space and $A$ a subspace. If we take $c\in C_n(X,A)=\frac{C_n(X)}{C_n(A)}$ then $c=j(b)$ for $b\in C_n(X)$ where $j$ is the quotient map $C_n(X)\longrightarrow C_n(X,A)$ because $j$ is onto. Then we take the boundary of $b$ and we get an element $\partial b\in C_{n-1}(X)$.

I'm fine until this point but then it goes on to say that $\partial b \in Ker j$ because $j(\partial b)=\partial (j(b)) = \partial c = 0$ and I don't understand why $\partial c = 0$.

Thanks for any help.

It seems you missed that Hatcher says "let $c\in C_n$ be a cycle" (emphasis mine).