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Objective: To investigate the relationship between the topography of amyloid‐β plaques, tau neurofibrillary tangles, and the overlap between the two, with cognitive dysfunction in individuals without dementia. Methods: We evaluated 154 individuals who were assessed with amyloid‐β PET with [18F]AZD4694, tau‐PET with [18F]MK6240, structural MRI, and neuropsychological testing. We also evaluated an independent cohort of 240 individuals who were assessed with amyloid‐β PET with [18F]Florbetapir, tau‐PET with [18F]Flortaucipir, structural MRI, and neuropsychological testing. Using the VoxelStats toolbox, we conducted voxel‐wise linear regressions between amyloid‐PET, tau‐PET, and their interaction with cognitive function, correcting for age, sex, and years of education. Results: In both cohorts, we observed that tau‐PET standardized uptake value ratio in medial temporal lobes was associated with clinical dementia rating Sum of Boxes (CDR‐SoB) scores independently of local amyloid‐PET uptake (FWE corrected at p < 0.001). We also observed in both cohorts that in regions of the neocortex, associations between neocortical tau‐PET and clinical function were dependent on local amyloid‐PET (FWE corrected at p < 0.001). Interpretation: In medial temporal brain regions, characterized by the accumulation of tau pathology in the absence of amyloid‐β, tau had direct associations with cognitive dysfunction. In brain regions characterized by the accumulation of both amyloid‐β and tau pathologies such as the posterior cingulate and medial frontal cortices, tau's relationship with cognitive dysfunction was dependent on local amyloid‐β concentrations. Our results provide evidence that amyloid‐β in Alzheimer's disease influences cognition by potentiating the deleterious effects of tau pathology. [ABSTRACT FROM AUTHOR]