If $A$ and $B$ are finite sets and $A \subset B$,then

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

$A$ die is thrown. Describe the following events: $A$: a number less than $7$,$B$: a number greater than $7$. Find $A \cap B$.

Let $A = \{a, e, i, o, u\}$ and $B = \{a, i, u\}$. Show that $A \cup B = A$.

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