We generalize the DeGroot model for opinion dynamics to better capture realistic social scenarios. We introduce a model where each agent has their own individual cognitive biases. Society is represented as a directed graph whose edges indicate how much agents influence one another. Biases are represented as the functions in the square region [-1,1] and categorized into four sub-regions based on the potential reactions they may elicit in an agent during instances of opinion disagreement. Under the assumption that each bias of every agent is a continuous function within the region of receptive but resistant reactions (R), we show that the society converges to a consensus if the graph is strongly connected. Under the same assumption, we also establish that the entire society converges to a unanimous opinion if and only if the source components of the graph-namely, strongly connected components with no external influence-converge to that opinion. We illustrate that convergence is not guaranteed for strongly connected graphs when biases are either discontinuous functions in or not included in R. We showcase our model through a series of examples and simulations, offering insights into how opinions form in social networks under cognitive biases.