Let $A = \{1, 2, 3, 4\}$ and $B = \{2, 3, 4, 5, 6\}$. Then $A \cap B$ is equal to:

Let $X$ be a non-empty set and let $P(X)$ denote the collection of all subsets of $X$. Define $f: X \times P(X) \rightarrow R$ by $f(x, A) = \begin{cases} 1, & \text{if } x \in A \\ 0, & \text{if } x \notin A \end{cases}$. Then,$f(x, A \cup B)$ equals

Let $A$ and $B$ be two sets in a universal set $U$. Then $A - B$ is equal to:

State whether the following statement is true or false. Justify your answer.
${2, 6, 10, 14}$ and ${3, 7, 11, 15}$ are disjoint sets.

Find the union of each of the following pairs of sets:
$A = \{ x : x \text{ is a natural number and } 1 < x \le 6 \}$
$B = \{ x : x \text{ is a natural number and } 6 < x < 10 \}$

If $P, Q$ and $R$ are subsets of a set $A$,then $R \times (P^c \cup Q^c)^c =$