Question Number 154407 by aaaspots last updated on 18/Sep/21
$${How}\:{to}\:{do}\:{it}\:{by}\:\subset\:{and}\:\supset\:? \\ $$
Commented by aaaspots last updated on 18/Sep/21
Commented by puissant last updated on 20/Sep/21
![1) ∪_(x∈[0;1]) [x−1;x+1] = [−1;1]∪[0;2]=[−1;2] 2) ∩_(x∈[0;1]) [x−1;x+1] = [−1;1]∩[0;2]=[0;1].](Q154410.png)
$$\left.\mathrm{1}\right) \\ $$$$\:\:\underset{{x}\in\left[\mathrm{0};\mathrm{1}\right]} {\cup}\:\left[{x}−\mathrm{1};{x}+\mathrm{1}\right]\:=\:\left[−\mathrm{1};\mathrm{1}\right]\cup\left[\mathrm{0};\mathrm{2}\right]=\left[−\mathrm{1};\mathrm{2}\right] \\ $$$$\left.\mathrm{2}\right) \\ $$$$\:\underset{{x}\in\left[\mathrm{0};\mathrm{1}\right]} {\cap}\:\left[{x}−\mathrm{1};{x}+\mathrm{1}\right]\:=\:\left[−\mathrm{1};\mathrm{1}\right]\cap\left[\mathrm{0};\mathrm{2}\right]=\left[\mathrm{0};\mathrm{1}\right]. \\ $$