Let $A = \{1, 2, 3, 4, 5, 6\}$. Insert the appropriate symbol $\in$ or $\notin$ in the blank space:
$10 \dots A$

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 $\leq 5$.
State true or false: (give reason for your answer)
Statement: $A$ and $B^{\prime}$ are mutually exclusive.

State whether the following set is finite or infinite:
The set of lines which are parallel to the $x$-axis.

Let $A$ and $B$ be two non-empty subsets of a set $X$ such that $A$ is not a subset of $B$. Then:

Which set is the subset of all given sets?

The remainder obtained when the polynomial $1 + x + x^3 + x^9 + x^{27} + x^{81} + x^{243}$ is divided by $x - 1$ is