The isospin asymmetries of $B to K^{(*)}mu^+mu^-$ decays and the partial branching fractions of $B^0 to K^0mu^+mu^-$ and $B^+ to K^{*+}mu^+mu^-$ are measured as a function of the di-muon mass squared $q^2$ using an integrated luminosity of 1.0 fb$^{-1}$ collected with the LHCb detector. The $B to Kmu^+mu^-$ isospin asymmetry integrated over $q^2$ is negative, deviating from zero with over 4 $sigma$ significance. The $B to K^{*}mu^+mu^-$ decay measurements are consistent with the Standard Model prediction of negligible isospin asymmetry. The observation of the decay $B^0 to K^0_{rmscriptscriptstyle S}mu^+mu^-$ is reported with 5.7 $sigma$ significance. Assuming that the branching fraction of $B^0 to K^0mu^+mu^-$ is twice that of $B^0 to K^0_{rmscriptscriptstyle S}mu^+mu^-$, the branching fractions of $B^0 to K^0mu^+mu^-$ and $B to K^{*+}mu^+mu^-$ are found to be ($0.31^{+0.07}_{-0.06}) times 10^{-6}$ and ($1.16pm0.19) times 10^{-6}$, respectively.
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