Show that $A \cap B=A \cap C$ need not imply $B = C$
Find the intersection of each pair of sets :
$X=\{1,3,5\} Y=\{1,2,3\}$
$A$ 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 $X$ and $Y$ are two sets such that $X$ has $40$ elements, $X \cup Y$ has $60$ elements and $X$ $\cap\, Y$ has $10$ elements, how many elements does $Y$ have?
Let $A=\{1,2,3,4,5,6,7,8,9,10\}$ and $B=\{2,3,5,7\} .$ Find $A \cap B$ and hence show that $A \cap B = B$