Basic confusion regarding definition of relative homology group $H_p(K;L)$ I am currently self-studying "Topology and Geometry for Physicists" by Nash and Sen, and have encountered a confusion regarding the definition of the relative homology group $H_p(K;L)$. The definition given is as follows :
The relative $p$-dimensional homology group of $K$ modulo $L$ is the quotient group
$$H_p(K;L) = Z_p(K;L)/B_p(K;L),p > 0$$
The members of $H_p(K;L)$ are $z_p+ C_p(L)$ (where as I understand it $z_p \in Z_p(K;L))$. 
My question is : Why are the elements of $H_p(K;L)$ not given by $z_p + B_p(K;L)$ (using the definition of the quotient group)?
Any help would be greatly appreciated keeping in mind that I am a beginner in homology. 

As you say, this statement is incorrect.  What I would guess is actually meant is that the elements of $Z_p(K;L)$ are of the form $z_p+C_p(L)$ (where $z_p\in C_p(K)$), since $Z_p(K;L)\subseteq C_p(K;L)=C_p(K)/C_p(L)$.  An element of $H_p(K;L)$ is then represented by an element of $Z_p(K;L)$ which has this form, modulo $B_p(K;L)$.
