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 $A \subset C$
Given the sets $A=\{1,3,5\}, B=\{2,4,6\}$ and $C=\{0,2,4,6,8\},$ which of the following may be considered as universal set $(s)$ for all the three sets $A$, $B$ and $C$
$\{0,1,2,3,4,5,6,7,8,9,10\}$
Assume that $P(A)=P(B) .$ Show that $A=B$.
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 subsets of the set $\{-1,0,1\}.$