If $A = \{2, 3, 4, 8, 10\}, B = \{3, 4, 5, 10, 12\}, C = \{4, 5, 6, 12, 14\}$ then $(A \cap B) \cup (A \cap C)$ is equal to

- A
$\{3, 4, 10\}$

- B
$\{2, 8, 10\}$

- C
$\{4, 5, 6\}$

- D
$\{3, 5, 14\}$

If $A=\{3,5,7,9,11\}, B=\{7,9,11,13\}, C=\{11,13,15\}$ and $D=\{15,17\} ;$ find

$A \cap D$

Find the union of each of the following pairs of sets :

$A=\{a, e, i, o, u\} B=\{a, b, c\}$

Show that $A \cap B=A \cap C$ need not imply $B = C$

If $X$ and $Y$ are two sets such that $X$ has $40$ elements, $X \cup Y$ has $60$ elements and $X$ $\cap\, Y$ has $10$ elements, how many elements does $Y$ have?

If the sets $A$ and $B$ are defined as $A = \{ (x,\,y):y = {e^x},\,x \in R\} $; $B = \{ (x,\,y):y = x,\,x \in R\} ,$ then