Through careful observation and deduction, she pieced together what had happened.

deduction 是名词，来自动词 deduce（推断、推论）。de- 是前缀表示"向下、彻底"，-duce 来自拉丁词根 ducere 表示"引导"。deduction 字面意思是"向下引导得出结论"，即"推理、推论"的过程。