Let $S = \{0, 1, 5, 4, 7\}$. Then the number of all subsets of $S$ is:

Find sets $A, B$ and $C$ such that $A \cap B, B \cap C$ and $A \cap C$ are non-empty sets and $A \cap B \cap C = \varnothing$.

State whether the following set is finite or infinite:
The set of letters in the English alphabet.

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 a universal set for all the three sets $A$,$B$ and $C$?
$X = \{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10\}$

Examine whether the following statement is true or false:
$\{a, b\} \not\subset \{b, c, a\}$

If $A = \{ 1, 2, 3, 4, 5 \}$,then what is the number of proper subsets of $A$?