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

If $A = \{3, 5, 7, 9, 11\}$,$B = \{7, 9, 11, 13\}$,$C = \{11, 13, 15\}$,and $D = \{15, 17\}$,find $(A \cap B) \cap (B \cup C)$.

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 $C \cap D$.

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

In a school,there are three types of games to be played. Some students play two types of games,but none play all three games. Which Venn diagram$(s)$ can justify the above statement?

State whether the following statement is true or false. Justify your answer.
${a, e, i, o, u}$ and ${a, b, c, d}$ are disjoint sets.