Examine whether the following statements are true or false :

$\{ x:x$ is an even natural number less than $6\}  \subset \{ x:x$ is a natural mumber which divide $36\} $

Let $S=\{1,2,3, \ldots, 40)$ and let $A$ be a subset of $S$ such that no two elements in $A$ have their sum divisible by 5 . What is the maximum number of elements possible in $A$ ?

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

$\{1,2,3\}\subset A$

Which of the following pairs of sets are equal ? Justify your answer.

$A = \{ \,n:n \in Z$ and ${n^2}\, \le \,4\,\} $ and $B = \{ \,x:x \in R$ and ${x^2} - 3x + 2 = 0\,\} .$

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 $A \subset B$ and $B \in C,$ then $A \in C$

List all the elements of the following sers :

$C = \{ x:x$ is an integer ${\rm{; }}{x^2} \le 4\} $