The nuclear dependence of the inclusive inelastic electron scattering cross section (the EMC effect) has been measured for the first time in $^{10}$B and $^{11}$B. Previous measurements of the EMC effect in $A \leq 12$ nuclei showed an unexpected nuclear dependence; $^{10}$B and $^{11}$B were measured to explore the EMC effect in this region in more detail. Results are presented for $^9$Be, $^{10}$B, $^{11}$B, and $^{12}$C at an incident beam energy of 10.6~GeV. The EMC effect in the boron isotopes was found to be similar to that for $^9$Be and $^{12}$C, yielding almost no nuclear dependence in the EMC effect in the range $A=4-12$. This represents important, new data supporting the hypothesis that the EMC effect depends primarily on the local nuclear environment due to the cluster structure of these nuclei.
