Question Number 145459 by syamilkamil1 last updated on 05/Jul/21
$${prove}\:\left({A}\:−\:{B}\right)−{C}\:=\:{A}\:−\left({B}\:\cup\:{C}\right) \\ $$
Answered by liberty last updated on 05/Jul/21
$$\:{A}−{B}={A}\cap{B}^{{c}} \\ $$$$\Rightarrow\left({A}−{B}\right)−{C}\:=\:\left({A}\cap{B}^{{c}} \right)\cap{C}^{{c}} \: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\:{A}\cap\left({B}^{{c}} \cap{C}^{{c}} \right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\:{A}\cap\left({B}\cup{C}\right)^{{c}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\:{A}−\left({B}\cup{C}\right)\: \\ $$
Commented by syamilkamil1 last updated on 07/Jul/21
$${thanks}\:{Sir} \\ $$