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**zpwnchen** Can you please check if they are correct?

a. $\displaystyle \emptyset \subset ${0} <-- True True, the empty set is a subset of every set

b. $\displaystyle \emptyset \subset ${$\displaystyle \emptyset $,{0}} <-- True True

c. {$\displaystyle \emptyset $}$\displaystyle \in ${$\displaystyle \emptyset$} <-- True No, it's false. $\displaystyle \color{red}\{\emptyset\}=\{\emptyset\}$

d. { $\displaystyle \emptyset$ } $\displaystyle \in$ {{ $\displaystyle \emptyset$ }} <-- False No, it's true. It is always true that $\displaystyle \color{red}\{x\}\in\{\{x\}\}$ whatever $\displaystyle \color{red}x$ may stand for.

e. {$\displaystyle \emptyset $} $\displaystyle \subset $ {$\displaystyle \emptyset $ , {$\displaystyle \emptyset $}} <-- True True

f. {{$\displaystyle \emptyset $}} $\displaystyle \subset $ {$\displaystyle \emptyset $,{$\displaystyle \emptyset $}} <--False No, it's true: $\displaystyle \color{red}\{\{x\}\}\subset\{\emptyset,\{x\}\}$

g. {{$\displaystyle \emptyset $}} $\displaystyle \subset $ {{$\displaystyle \emptyset $},{$\displaystyle \emptyset $}} <--False Correct, it is false, it should be $\displaystyle \color{red}\{\{\emptyset\}\}\subseteq\{\{\emptyset \},\{\emptyset\}\}$ or $\displaystyle \color{red}\{\{\emptyset\}\}=\{\{\emptyset\},\{\em ptyset\}\}$

Thank you