If $A, B, C$ are three sets, then $A \cap (B \cup C)$ is equal to

- A
$(A \cup B) \cap (A - C)$

- B
$(A \cap B) \cup (A \cap C)$

- C
$(A \cup B) \cup (A \cup C)$

- D
None of these

If $A, B$ and $C$ are three sets such that $A \cap B = A \cap C$ and $A \cup B = A \cup C$ then

- [AIEEE 2009]

Let $A =\{1,2,3,4,5,6,7\}$ and $B =\{3,6,7,9\}$. Then the number of elements in the set $\{ C \subseteq A : C \cap B \neq \phi\}$ is

- [JEE MAIN 2022]

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

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

State whether each of the following statement is true or false. Justify you answer.

$\{2,6,10\}$ and $\{3,7,11\}$ are disjoint sets.

If $A$ and $B$ are any two sets, then $A \cap (A \cup B)$ is equal to