$A$ and $B$ are two subsets of set $S$ = $\{1,2,3,4\}$ such that $A\ \cup \ B$ = $S$ , then number of ordered pair of $(A, B)$ is 

If the sets $A$ and $B$ are defined as $A = \{ (x,\,y):y = {1 \over x},\,0 \ne x \in R\} $ $B = \{ (x,y):y =  - x,x \in R\} $, then

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

Using that for any sets $\mathrm{A}$ and $\mathrm{B},$

$A \cup(A \cap B)=A$

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

$A = \{ x:x$ is a natural number and multiple of $3\} $

$B = \{ x:x$ is a natural number less than $6\} $