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Intuition, induction, and deduction are types of reasoning used in geometry. Deduction uses logic to form a conclusion based on given statements.
intuition
An antonym for intuition (instinctive or emotional sense) would be reasoning (logical sense).
Example sentence - There is no reasoning with horrid adult children. You could be reasoning with irrational people.
Intuition is the ability to understand things without the need for reasoning. In natural science using empirical method, in mathematics it is based on previous layers of knowledge including laws and foundation, and in social science it leads to human behavior and trends..