Let $A$ and $B$ be sets. If $A \cap X=B \cap X=\phi$ and $A \cup X=B \cup X$ for some set $X ,$ show that $A = B$

( Hints $A = A \cap (A \cup X),B = B \cap (B \cup X)$ and use Distributive law )

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

$A \cap B$

If $A$ and $B$ are not disjoint sets, then $n(A \cup B)$ is equal to

Let $A$ and $B$ be subsets of a set $X$. Then

Let $A$ and $B$ be two sets in the universal set. Then $A – B$ equals