  Classical and quantum Friedmann-Lema\^itre-Robertson-Walker universes filled
with non-interacting radiation and dust fluids are considered in the framework
of Ho\v{r}ava-Lifshitz gravity theory. The Ho\v{r}ava-Lifshitz theory is set in
its projectable version and without detailed balance condition. Canonical
quantization is performed in the Wheeler-DeWitt approach of quantum cosmology
for a minisuperspace model in the light of de Broglie-Bohm interpretation of
quantum mechanics. The main results are analytical solutions for non-singular
quantum bounce and cyclic universes for open and closed spatial sections in
terms of the parameters of Ho\v{r}ava-Lifshitz theory.
