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.
Similar Questions
Consider the sets
$\phi, A=\{1,3\}, B=\{1,5,9\}, C=\{1,3,5,7,9\}$
Insert the symbol $\subset$ or $ \not\subset $ between each of the following pair of sets:
$A, \ldots B$
Consider the sets
$\phi, A=\{1,3\}, B=\{1,5,9\}, C=\{1,3,5,7,9\}$
Insert the symbol $\subset$ or $ \not\subset $ between each of the following pair of sets:
$A, \ldots B$
List all the elements of the following sers :
$E = \{ x:x$ is a month of a year not having $ 31 $ days ${\rm{ }}\} $
List all the elements of the following sers :
$E = \{ x:x$ is a month of a year not having $ 31 $ days ${\rm{ }}\} $
Which of the following are sets ? Justify your answer.
The collection of all boys in your class.
Which of the following are sets ? Justify your answer.
The collection of all boys in your class.
In the following state whether $A=B$ or not :
$A=\{a, b, c, d\} ; B=\{d, c, b, a\}$
In the following state whether $A=B$ or not :
$A=\{a, b, c, d\} ; B=\{d, c, b, a\}$
Write the following sets in the set-builder form :
$\{ 3,6,9,12\}$
Write the following sets in the set-builder form :
$\{ 3,6,9,12\}$