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

Which of the following Venn diagrams corresponds to the statement "All mothers are women"? ($M$ is the set of all mothers,$W$ is the set of all women)

If $A = \{ x : x \text{ is a natural number} \}$,$B = \{ x : x \text{ is an even natural number} \}$,$C = \{ x : x \text{ is an odd natural number} \}$ and $D = \{ x : x \text{ is a prime number} \}$,find $B \cap C$.

Let $A = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\}$ and $B = \{2, 3, 5, 7\}$. Find $A \cap B$ and hence show that $A \cap B = B$.

If $X = \{a, b, c, d\}$ and $Y = \{f, b, d, g\},$ find $X \cap Y$.

$A$ class has $175$ students. The following data shows the number of students opting for one or more subjects: Mathematics $100$,Physics $70$,Chemistry $40$; Mathematics and Physics $30$,Mathematics and Chemistry $28$,Physics and Chemistry $23$; Mathematics,Physics,and Chemistry $18$. How many students have opted for Mathematics alone?