The Short Version
This claim is a well-known neuromyth. While some hemispheric specialization exists — the left hemisphere contributes more to language processing, for example — modern neuroscience consistently shows that both logic and creativity involve extensive collaboration between both hemispheres. Large-scale fMRI studies find no evidence of global hemispheric dominance for these functions. Creativity in particular relies on bilateral brain networks, and some studies even show increased left-hemisphere activity during creative tasks. The word "primarily" makes this claim false.