Write down all the subsets of the following set: $\{a\}$

Make correct statements by filling in the symbols $\subset$ or $\not\subset$ in the blank spaces:
${2,3,4} \dots {1,2,3,4,5}$

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 the pair of sets: $B \dots C$.

Show that the set of letters needed to spell "$CATARACT$" and the set of letters needed to spell "$TRACT$" are equal.

Two dice are thrown. The events $A, B$ and $C$ are as follows:
$A:$ getting an even number on the first die.
$B:$ getting an odd number on the first die.
$C:$ getting the sum of the numbers on the dice $\leq 5$.
Describe the event $A$ or $B$.

What is the remainder when the polynomial $P(x) = 1 + x + x^3 + x^9 + x^{27} + x^{81} + x^{243}$ is divided by $x - 1$?