Write the following as intervals :

 $\{ x:x \in R, – 4\, < \,x\, \le \,6\} $

In each of the following, determine whether the statement is true or false. If it is true, prove it. If it is false, give an example.

If $x \in A$ and $A \not\subset B$, then $x \in B$

In each of the following, determine whether the statement is true or false. If it is true, prove it. If it is false, give an example.

If $x \in A$ and $A \in B,$ then $x \in B$

Let $A=\{1,2,\{3,4\}, 5\} .$ Which of the following statements are incorrect and why ?

$\{ 3,4\}  \subset A$

If $A$ and $B$ are any two non empty sets and $A$ is proper subset of $B$. If $n(A) = 4$, then minimum possible value of $n(A \Delta B)$ is (where $\Delta$ denotes symmetric difference of set $A$ and set $B$)