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

For two sets $A$ and $B$,$A \cup B = A$ if and only if

Let $x_{1}, x_{2}, \ldots, x_{15}$ be $15$ distinct numbers chosen from $1, 2, 3, \ldots, 15$. Then, the value of $(x_{1}-1)(x_{2}-1)(x_{3}-1) \ldots (x_{15}-1)$ is

Are the following pair of sets equal? Give reasons.
$A = \{ 2, 3 \}, \quad B = \{ x : x \text{ is a solution of } x^2 + 5x + 6 = 0 \}$

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

State which of the following sets are finite or infinite:
$\{ x : x \in N \text{ and } x \text{ is odd} \}$