State whether each of the following set is finite or infinite :

The set of circles passing through the origin $(0,0)$

Consider the sets

$\phi, A=\{1,3\}, B=\{1,5,9\}, C=\{1,3,5,7,9\}$

Insert the symbol $\subset$ or $ \not\subset $ between each of the following pair of sets:

$\phi \,....\,B$

Examine whether the following statements are true or false :

$\{ a,b\}  \not\subset \{ b,c,a\} $

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

$\{ \{ 3,4\} \}  \subset A$

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

$\{ 3,4\}  \subset A$

Let $S=\{1,2,3,4\}$. The total number of unordered pairs of disjoint subsets of $S$ is equal to