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:

$A \ldots C$

Let $A, B,$ and $C$ be the sets such that $A \cup B=A \cup C$ and $A \cap B=A \cap C$. Show that $B = C$

Examine whether the following statements are true or false :

$\{ a,b\}  \not\subset \{ b,c,a\} $

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

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 $C$

$\{ 1,2,3,4,5,6,7,8\} $