If $A = \{1, 2, 3, 4\}, B = \{3, 4, 5, 6\}, C = \{5, 6, 7, 8\}$ and $D = \{7, 8, 9, 10\}$,find $B \cup D$.

If $A$ and $B$ are two sets such that $A \subset B$,then what is $A \cup B$?

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:

If $A = \{1, 2, 3\}$,$B = \{3, 4\}$,and $C = \{4, 5, 6\}$,then find $A \cup (B \cap C)$.

Let $E, F$ and $G$ be three events having probabilities $P(E) = \frac{1}{8}, P(F) = \frac{1}{6}$ and $P(G) = \frac{1}{4}$,and let $P(E \cap F \cap G) = \frac{1}{10}$. For any event $H$,if $H^C$ denotes its complement,then which of the following statements is(are) $TRUE$?
$(A) P(E \cap F \cap G^C) \leq \frac{1}{40}$
$(B) P(E^C \cap F \cap G) \leq \frac{1}{15}$
$(C) P(E \cup F \cup G) \leq \frac{13}{24}$
$(D) P(E^C \cap F^C \cap G^C) \leq \frac{5}{12}$