we introduce deductive association networks(DANs), a network that performs deductive reasoning. To have high-dimensional thinking, combining various axioms and putting the results back into another axiom is necessary to produce new relationships and results. For example, it would be given two propositions:"Socrates is a man."and"All men are mortals."and two propositions could be used to infer the new proposition,"Therefore Socrates is mortal.". To evaluate, we used MNIST Dataset, a handwritten numerical image dataset, to apply it to the group theory and show the results of performing deductive learning.