If $A \cap B = B$,then

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

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: $B \dots C$.

Which of the following sets is a subset of all other sets?

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

Two sets $A$ and $B$ are disjoint if and only if