State whether the following statement is true or false. Justify your answer.
${2, 6, 10}$ and ${3, 7, 11}$ are disjoint sets.

Let $a > 0, a \neq 1$. Then,the set $S$ of all positive real numbers $b$ satisfying $(1+a^2)(1+b^2) = 4ab$ is

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:

Which of the following pairs of sets are disjoint?
$A = \{ x : x \text{ is an even integer} \}$
$B = \{ x : x \text{ is an odd integer} \}$

Let $P$ and $T$ be the subsets of the $xy$-plane defined by $P = \{(x, y) : x > 0, y > 0 \text{ and } x^2 + y^2 = 1\}$ and $T = \{(x, y) : x > 0, y > 0 \text{ and } x^8 + y^8 < 1\}$. Then,$P \cap T$ is

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