Which of the following are sets ? Justify your answer.

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

Examine whether the following statements are true or false :

$\{a\} \subset\{a, b, c\}$

In the following state whether $\mathrm{A = B}$ or not :

$A = \{ x:x$ is a multiple of $10\} ;B = \{ 10,15,20,25,30 \ldots  \ldots \} $

State which of the following sets are finite or infinite :

$\{ x:x \in N$ and $2x - 1 = 0\} $

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\} $

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 $A \in C$