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.
Write down all the subsets of the following sets
$\{ 1,2,3\} $
Let $A=\{1,2,\{3,4\}, 5\} .$ Which of the following statements are incorrect and why ?
$\{1,2,5\}\subset A$
Which of the following are sets ? Justify your answer.
The collection of questions in this chapter.
Are the following pair of sets equal ? Give reasons.
$A = \{ 2,3\} ,\quad \,\,\,B = \{ x:x$ is solution of ${x^2} + 5x + 6 = 0\} $
Which of the following are sets ? Justify your answer.
A collection of most dangerous animals of the world.