Let $A$ and $B$ be subsets of a set $X$. Then
$A - B = A \cup B$
$A - B = A \cap B$
$A - B = {A^c} \cap B$
$A - B = A \cap {B^c}$
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 $\mathrm{R}$ is the set of real numbers and $\mathrm{Q}$ is the set of rational numbers, then what is $\mathrm{R - Q} ?$
If $X$ and $Y$ are two sets such that $n( X )=17, n( Y )=23$ and $n( X \cup Y )=38$
find $n( X \cap Y )$
If $A=\{3,5,7,9,11\}, B=\{7,9,11,13\}, C=\{11,13,15\}$ and $D=\{15,17\} ;$ find
$A \cap B$
Find the union of each of the following pairs of sets :
$A=\{1,2,3\}, B=\varnothing$