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deduce (v.)

early 15c., deducen, "to show, prove, demonstrate;" late 15c., "to deduct," from Latin deducere "lead down, derive" (in Medieval Latin, "infer logically"), from de "down" (see de-) + ducere "to lead" (from PIE root *deuk- "to lead"). The usual modern sense of "draw a conclusion from something already known" is first recorded 1520s, from Medieval Latin. Related: Deduced; deducing.

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Definitions of deduce from WordNet

deduce (v.)
reason by deduction; establish by deduction;
Synonyms: infer / deduct / derive
deduce (v.)
conclude by reasoning; in logic;
Synonyms: infer
From wordnet.princeton.edu