Let $A, B$ and $C$ be three sets. If $A \in B$ and $B \subset C$, is it true that $A$ $\subset$ $C$ ?. If not, give an example.
Let $A, B$ and $C$ be three sets. If $A \in B$ and $B \subset C$, is it true that $A$ $\subset$ $C$ ?. If not, give an example.
No. Let $A=\{1\}, B=\{\{1\}, 2\}$ and $C=\{\{1\}, 2,3\} .$ Here $A \in B$ as $A=\{1\}$ and $B \subset C$. But $A \not\subset C$ as $1 \in A$ and $1 \notin C$
Note that an element of a set can never be a subset of itself.
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