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

In this question,all integers are represented in base $10$. Consider the set $E$ of positive integers $n$ having the property that when any nonzero digit $d \in \{1, 2, \dots, 9\}$ is written to the right of $n$,the resulting number is divisible by $d$. Let $N$ be the smallest element of $E$. The product of the digits of $N$ is:

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

In the following,state whether $A = B$ or not:
$A = \{2, 4, 6, 8, 10\}$; $B = \{x : x \text{ is a positive even integer and } x \le 10\}$

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

Which of the following is a true statement?