Counting tuples restricted by coprimality conditions

Given a set $A=\{(i_1,j_1),\dots ,(i_m,j_m)\}$ we say that $(a_1,\dots ,a_v)$ exhibits pairwise coprimality if $\gcd (a_i,a_j)=1$ for all $(i,j)\in A$. For a given positive $x$ we give an asymptotic formula for the number of $(a_1,\dots ,a_v)$ with $1\le a_1,\dots ,a_v\le x$ that exhibit pairwise coprimality. Our error term is better than that of Hu.