The shaded region in the given figure is

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

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

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

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

Show that for any sets $\mathrm{A}$ and $\mathrm{B}$, $A=(A \cap B) \cup(A-B)$ and $A \cup(B-A)=(A \cup B).$

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]

Which of the following pairs of sets are disjoint

$\{1,2,3,4\}$ and $\{ x:x$ is a natural number and $4\, \le \,x\, \le \,6\} $

Show that $A \cup B=A \cap B$ implies $A=B$.

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