Let $A = \{1, 2, \{3, 4\}, 5\}$. Which of the following statements is incorrect and why?
$\{\varnothing\} \subset A$
$\{\varnothing\} \subset A$
(A) Given the set $A = \{1, 2, \{3, 4\}, 5\}$.
The statement $\{\varnothing\} \subset A$ is incorrect.
For $\{\varnothing\}$ to be a subset of $A$,the element $\varnothing$ must be an element of $A$ (i.e.,$\varnothing \in A$).
However,the elements of $A$ are $1, 2, \{3, 4\},$ and $5$. None of these elements is the empty set $\varnothing$.
Therefore,$\varnothing \notin A$,which implies that $\{\varnothing\}$ is not a subset of $A$.
The statement $\{\varnothing\} \subset A$ is incorrect.
For $\{\varnothing\}$ to be a subset of $A$,the element $\varnothing$ must be an element of $A$ (i.e.,$\varnothing \in A$).
However,the elements of $A$ are $1, 2, \{3, 4\},$ and $5$. None of these elements is the empty set $\varnothing$.
Therefore,$\varnothing \notin A$,which implies that $\{\varnothing\}$ is not a subset of $A$.
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