Write down all the subsets of the following sets

$\{ 1,2,3\} $

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

$ 0\, ........\, A $

State which of the following sets are finite or infinite :

$\{ x:x \in N$ and ${x^2} = 4\} $

State which of the following sets are finite or infinite :

$\{ x:x \in N$ and $x$ is prime $\} $

Examine whether the following statements are true or false :

$\{ a,b\}  \not\subset \{ b,c,a\} $

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 $x \in B$