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

Make correct statements by filling in the symbols $\subset$ or $ \not\subset $ in the blank spaces:

$\{ x:x$ is a triangle in a plane $\}  \ldots \{ x:x$ is a rectangle in the plane $\} $

List all the elements of the following sers :

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

Which of the following are sets ? Justify your answer.

The collection of all the months of a year beginning with the letter $\mathrm{J}.$

Let $A=\{1,2,3,4,5,6\} .$ Insert the appropriate symbol $\in$ or $\notin$ in the blank spaces:

$ 4\, ......... \, A $

Assume that $P(A)=P(B) .$ Show that $A=B$.