If $$A=\{1,{\{\emptyset}\}\}$$
then is $$B={\{\emptyset}\} \subseteq A?$$
I would say yes it is because it is the set containing the empty set, but the solution says it is not. Why is this?
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Sign up to join this communityIf $$A=\{1,{\{\emptyset}\}\}$$
then is $$B={\{\emptyset}\} \subseteq A?$$
I would say yes it is because it is the set containing the empty set, but the solution says it is not. Why is this?
The solution is correct: it is not. In order for $B$ to be a subset of $A$, every element of $B$ must be an element of $A$. What are the elements of $B$? There is only one, $\varnothing$. What are the elements of $A$? $1$ and $\{\varnothing\}$. Neither of these is $\varnothing$, so $\varnothing\notin A$, and therefore $B\nsubseteq A$. Note that $\varnothing$, the element of $B$, and $\{\varnothing\}$, one of the elements of $A$, are not the same thing: $\varnothing$ is a set with no members, and $\{\varnothing\}$ is a set with one member, that one member being the set $\varnothing$.