Question Number 159300 by saly last updated on 15/Nov/21
Answered by Derrick last updated on 15/Nov/21
$${preve} \\ $$$$\left.{a}\right){montrons}\:{par}\:{double}\:{inclusion} \\ $$$${soit}\:{x} \\ $$$${x}\in{f}^{−\mathrm{1}} \:\left({A}\cup{B}\right)\Leftrightarrow{f}\left({x}\right)\in\left({A}\cup{B}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\Leftrightarrow{f}\left({x}\right)\in{A}\:{ou}\:{f}\left({x}\right)\in{B} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\Leftrightarrow{x}\in{f}^{−\mathrm{1}} \left({A}\right)\:{ou}\:{x}\in{f}^{−\mathrm{1}} \left({B}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\Leftrightarrow{x}\in\left({f}^{−\mathrm{1}} \left({A}\right)\cup{f}^{−\mathrm{1}} \left({B}\right)\right. \\ $$$$ \\ $$